There are two common misconceptions about the University of Buckingham. One is that it is a "Thatcherite" institution - the Iron Lady was the second chancellor (1992-99) and a striking portrait of her greets visitors in the reception area - that was set up as an experiment in very different times and is now just a harmless irrelevance. The other view is that it is a dangerous nest of fire-breathing and offensive reactionaries who would not - and probably should not - be welcome anywhere else.

Neither is entirely accurate. On a day-to-day level, its long terms, two-year degrees, high staff-to-student ratios and largely vocational courses in subjects such as business, accountancy and law mean that education in Britain's only private university is pretty intense. Students tend to be committed, and they consistently rate the experience very highly in the National Student Survey.

Yet Buckingham is far more than just a small university quietly doing its own thing. And that takes us back to its foundations, and the ideals of its charismatic and high-profile vice-chancellor, Terence Kealey.

Anyone who lived through the 1970s and 1980s will remember the programme of "rolling back the frontiers of the state" which was promoted by free-market think-tanks such as the Institute of Economic Affairs and then enjoyed a brief official vogue under Thatcher. This was one of the strands that led to the creation of Buckingham in 1976. Something of the tone of the times is well caught by an early recruit, Martin Ricketts, who describes himself as a classical liberal and now serves as dean of humanities.

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"I came because of extreme irritation with the dominance of the state within higher education," he says, "and the likelihood of increasing dominance. There was a great deal of resentment at the extent to which the state was interfering in all sorts of areas of the economy. And this needed to be reversed.

"It was a sort of principled thing, really. I've always been irritated at being told what to do. I liked the idea of a few eccentrics wanting to set up a private university - it was the fact that it was considered shocking that I thought was such bad news. In a free society, why shouldn't they? The fact it was so shocking made me want to give them some help," Ricketts says.

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Since Thatcherism is long gone and it is a particularly difficult time to be a "free-market fundamentalist" arguing for less state regulation, does this mean that Buckingham is built on values well past their sell-by date?

Kealey vociferously disputes the suggestion.

"You couldn't get much more ideological than me," he says cheerfully. "My book The Economic Laws of Scientific Research stated quite categorically that governments should not fund science or higher education. If I had my way, taxes would be a third of what they are now. I am absolutely what the Americans call a libertarian and we would call a classical liberal. The state nationalised the schools, the hospitals, the universities, social security - all (of which) I absolutely deplore. I believe in property rights and the rule of law and not much else.

"At Cambridge, I was out on an extreme limb. People liked me personally but found my views very difficult and potentially dangerous. More than one senior professor said that my proselytising about funding for science potentially damaged Cambridge when they were negotiating with the Government."

Such outspokenness also worried some of Kealey's colleagues when he arrived at Buckingham in 2001. "They saw this chap coming from Cambridge who was primarily a researcher and writing all this stuff about why governments shouldn't fund science - and they thought they were getting an ideologically motivated researcher who knew nothing about Buckingham. And to some extent they were right."

But instead of a hotbed of free marketers, Kealey found a place where, he says, "people are obsessed with teaching and the profession of being an academic".

"They see themselves as professionals independently prosecuting their profession because they are left alone to do so. This is an institution of internal exiles who are all in their minds 19th-century Oxbridge dons teaching without interference."

If one of the elements that came together to create Buckingham was libertarianism, another was a form of nostalgic traditionalism (see box, page 39). It is not a place, sniffed one academic, where we are likely to see equestrian studies or surfing in the prospectus any day soon.

These different elements are, of course, in a certain degree of tension with each other, and both are subject to the discipline of the market. "There is a kind of conservatism built into the university," agrees Ricketts, "but the market is a remorseless feature we have to cope with. How modish we get depends on how desperate we are."

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What would they do, he wonders aloud, in the unlikely event that "somebody from Dubai had a crush on Milton Keynes football club and wanted a chair in football studies - would we say no?"

"I don't know. I suspect we'd take the money."

Today, however, what has made Buckingham well known - and indeed notorious - is its outspoken vice-chancellor and a number of his equally provocative appointments.

Kealey is a fiercely eloquent defender of his university. When the Quality Assurance Agency (QAA) expressed "limited confidence ... in the soundness of (Buckingham's) current and likely future management of the academic standards of its awards" last October, Kealey argued in Times Higher Education that, although "Buckingham is the only university in Britain to engage voluntarily with the QAA", the university had come up against a form of "bureaucratic centralisation" that "institutionalises distrust".

"The QAA does not measure outcomes," he argued, "only bureaucracy."

Yet it is the people Kealey has assembled around him who, in the eyes of some, constitute a veritable rogues' gallery (see box, above).

Kealey says he is proud to provide "a home for people who are good but different - they have to be good, of course ... The reason why we're brave enough to do it is that, because we're not concerned about Hefce (Higher Education Funding Council for England) and the RAE (research assessment exercise), our council is not so worried about what the great and the good are thinking. So it's very much a policy. Let's just have the conversation, let's take the risks and see what emerges - I think that's what universities should be about."

But don't the mavericks he has taken on tend to occupy a limited part of the political spectrum? "That's only a consequence of the fact that the other part of the political spectrum is catered for by the other 138 universities," Kealey replies. "If you are on the Left and have a particular vision of the role of the state, you'll find lots of universities to give you a very comfortable home. What is not catered for is the kind of people you're describing. If I lived in a right-wing society, I would absolutely give voice to the Left and be proud of it."

One can, of course, dispute the views expressed by academics at Buckingham. But for anyone who can get over their disagreements, it remains a vibrant and fascinating place. It is never likely to be a model for the rest of the sector, but it does provide a sort of mirror. In Kealey's trenchant view, "5 to 10 per cent of the academy would secretly like to be in an independent university, if only it could be achieved (although they wouldn't know how to get there and certainly wouldn't want to run any risks)".

If this contains even a grain of truth, it makes Buckingham an important example, challenge or warning.

For those frustrated by Hefce and the RAE, Buckingham offers an image of what life might be like without them. Higher education looks very different to people who have largely worked within the state sector, but have left it and are now outsiders looking in, challenging preconceptions and sometimes (and why not?) deliberately setting out to provoke. And there must be something to be said for an institution where a visiting academic could describe his experience of arriving there in the words of an old hymn, "My chains fell off".

To find out more, the only thing to do is beard the dragons in their dens. As often happens, those who come over as pretty fierce in print turn out to be scrupulously polite and thoughtful in person. Anthony Glees, director of the Centre for Security and Intelligence Studies, for example, struggles to find practical ways to cope with the threat of Islamic terror while maintaining the rule of law.

"I would like a smaller state confined to the things only the state can do," he says. "It just so happens that the things that interest me - security and intelligence - are things that, as a matter of national policy, only the state should do. But I see it as my mission to help in the education and skilling-up of people who want to work in state agencies. My job is to make sure the state gets it right as often as possible. And I do think that we have an ever-more professional and better-educated intelligence and security community."

Yet Glees is disenchanted by what he sees in universities in the state sector, where he worked until this autumn. They have become, he says, "a conspiracy between students, the administration, the Government and the academics".

"Students could get their 2:1 degrees, academics could do their research without anybody bothering them, the administrators could administer until they were blue in the face and the Government could get people off the unemployment records."

Glees also feels that the range of debate has narrowed: "If you have a view, as I do, which is of the centre-right, then life is very uncomfortable for you."

As an example, he cites his failure to find a publisher for his "most recent research on Arab and Islamic funding of British universities amounting to ?150-160 million over the past ten years". He worries that this funding will lead to rival sectarian centres for Islamic studies, funded by Saudi and Iranian money, sometimes at the expense of prestigious existing centres devoted to the Middle East.

"So you see that state-run universities are taking unregulated money," Glees claims. "Political parties would, quite rightly, not be allowed to take such money for such purposes. And they are doing things it's not universities' jobs to do, like creating good relations between states. That's what we have diplomats for. However, I can't find a single think-tank that wants to publish this work. Why? Because it upsets Arab and Islamic funders, and because it's upsetting to our university system, which stands to lose a lot of money if regulation is brought in."

For Alan Smithers, director of the Centre for Education and Employment Research (who often works on projects with the deputy director, Pamela Robinson), "the great thing about the University of Buckingham is that it stands for independent thought." He believes that "we have overextended higher education" and that "it would be much more healthy for the universities of this country if those such as Oxbridge and the London School of Economics became independent."

But he also feels that there is a major structural problem, and that funding systems and the RAE have had a damaging impact on research, particularly in the field of education.

After years of producing apparently unnoticed research papers, he recalls, he "wrote an article for The Times and got an amazing response ... In science it makes sense to make precise measurements and then lodge them in journals for posterity, even if it takes a year or 18 months to be published. The model makes less sense in education, although that's the paradigm that underlies the RAE, which is assessed by people within that paradigm.

"In Buckingham, we can respond to the intrinsic requirements of research within a rapidly changing scene. We need to get information out to policymakers and practitioners as soon as possible. Peer-review journals are not effective in getting the message out. Educational research lives, a lot of the time, in its own bubble."

This is exacerbated by the need to take account of funders. "Education is a difficult area to research because it tends to be value-driven. One of the things we work at really hard is achieving an independent stance. And we're able to do that because of a plurality of funders - the National Union of Teachers, the Headmasters' and Headmistresses' Conference, the Government, various charitable foundations, and so on. In a lot of educational research," Smithers concludes provocatively, "the narrative comes first and the numbers come later."

What applies to research in particular is also relevant to higher education more generally. "It is good to be independent of the RAE - and more generally of the Government as a monopoly customer," he argues. "Universities should open themselves up more than they do. We could have targeted funding from the Government to ensure national interests such as sufficient numbers of teachers or research scientists. Business could invest in things they find important and students could fund things they want to do for fun.

"Buckingham is an interesting seedbed of what that would mean - and the country ought to be very grateful." He may have a long wait.

Geoffrey Alderman, Michael Gross professor of politics and contemporary history, thought he "had taken early retirement in December 2006 and a couple of months later Terence phoned me up and asked me to join him in Buckingham". Although he spent most of his academic life in the state sector, including 22 years at Royal Holloway, University of London, it was particularly while working at the University of Middlesex as head of quality (and later pro vice-chancellor) from 1994 to 1999 that, he says, "worries that I had always had about the effect of state funding of higher education on the academic process began to gel.

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"I had to deal with a succession of Hefce auditors and I found the breath of the Government down the neck of the university worrying - that the Government through the funding council was requiring the university to do certain things or not to do certain things. Widening participation is a wonderful concept. But it's not the purpose of a university to widen (or to narrow) participation, but to pursue the truth."

Escaping from this environment by taking a post as vice-president of Touro College in New York was, Alderman says, "a liberation".

He also fretted about the constraints on his freedom to speak out. "One time I was publicly critical of the QAA, although it was faithfully reported that I was speaking in a personal capacity. (Middlesex vice-chancellor) Michael Driscoll and I had a difference of opinion (about) whether it was possible for me to say something even in a personal capacity. I would like to think that the senior managers of state universities are not so beholden to the state that they have to say that everything is rosy in the garden."

A similar ticking off, at the time of a dispute between Thames Valley University (TVU) and the QAA, led Alderman to conclude that "British higher education does not understand the meaning of self-regulation".

"Had the TVU saga taken place in the US, every senior university manager would have been asked for a comment. But there is a sort of English reserve here - we mustn't talk about other people's troubles.

"If you attend the annual meetings of any of the six American regional accrediting commissions, at a certain point in the proceedings there will be a vote on institutions that have been found so derelict in their duty that the ultimate sanction of withdrawing accreditation needs to be taken. There's actually a vote and sometimes tears are shed. That's self-regulation."

Asked what it's like to work at a place such as Buckingham, where people are generally willing to speak their minds and do not care who they offend, Alderman responds simply: "This is a real university."

He claims that his forcefully expressed views have not prevented him from having perfectly good relations with Muslim students and community leaders. But isn't there also something tiresome and counterproductive about the stridency he and his colleagues sometimes go in for? It is not hard to find enthusiasts for the Buckingham model who refer to official British educational policy as "Soviet" or even "Stalinist". But only those who have led a pretty sheltered life could seriously compare Kenneth Clarke or Ruth Kelly to Joseph Stalin. Isn't the comparison not only ridiculous but offensive to Stalin's millions of victims?

"I don't think I've ever described Hefce as a Stalinist institution," replies Alderman without missing a beat. "And it would be offensive to do so - not very, but slightly."

MAVERICKS AND ICONOCLASTS

While small classes and high contact hours mean that many academics at Buckingham put most of their energies into teaching and student care, a number of recent recruits are well-known public figures whose views often attract criticism, controversy or dismay.

Bruce Charlton, professor of theoretical medicine, has said, in a research paper quoted in Times Higher Education, that "higher social classes have a significantly higher average IQ than lower social classes".

He dismisses as unproven claims that elite universities are "unfairly excluding people from low social-class backgrounds", and believes they have been used "to fuel a populist 'class war' agenda". Charlton has also been happy to refer to Marxism, feminism and postmodernism as "stupid academic fads".

Anthony Glees, director of the Centre for Security and Intelligence Studies, has argued in these pages that in the face of the threat from Islamic extremism, universities must ban "faith societies" and "establish watertight screening methods, together with MI5, to exclude dangerous students".

He believes the Government should abolish the clearing system - in which students gain last-minute admission to courses without full checks being made - as "a security threat" and even consider the option of internment.

Glees' book, The Stasi Files (2003), about British academics and others who acted as spies for the East German Government, has also attracted controversy.

Geoffrey Alderman, Michael Gross professor of politics and contemporary history, is a pugnacious polemicist in The Jewish Chronicle, and elsewhere, who wrote one piece entitled "Muslim dialogue? Don't bother", and responded to criticism with an article headed "My hostility to Islam is rational".

Chris Woodhead, Sir Stanley Kalms professor of education, is the controversial former chief inspector of schools and chairman of Cognita, which owns a chain of private schools. At Buckingham, he is involved in creating what amounts to a teacher training centre, supplying the equivalent of a PGCE (postgraduate certificate in education) for the independent sector.

Employed alongside him are two other well-known and outspoken educational pundits of a traditionalist mould, Anthony O'Hear and Alan Smithers.

NEW BEGINNINGS: AN IDEOLOGY TAKES SHAPE

The foundation of the University of Buckingham, its first dean of admissions has written, represented "a reaction against what appeared to be the dominant trends of the late 1960s and early 1970s". Yet even at the time, says John Clarke (now a member of the International Studies team), two rather different and potentially conflicting agendas were at work.

The first was a free-market economic agenda, hostile to state monopolies, which argued that an independent university would be less bureaucratic, and more efficient and businesslike, than the rest of the sector.

Some even argued that large endowments could make academics lazy and complacent, and that most or all of the income should therefore be derived directly from student fees.

But how could a private university hope to compete in the market with those where fees were subsidised by the state?

One possible model was an inner-city institution where students could live at home, facilities were used throughout the year and close to 24 hours a day, while staff had heavy teaching loads and few opportunities for research.

This was hardly a recipe for attracting high-calibre recruits from secure jobs in other universities.

The alternative agenda was more strictly academic. Leading scholars such as Max Beloff were inspired, writes Clarke, by "a streak of nostalgia or traditionalism, whose inspiration came ... from the Oxford of the 1930s". They were unsympathetic to student radicalism and lack of respect for academic and other authority common in the 1960s and they envisaged a sort of liberal-arts college where general degrees would always include some science and a foreign language.

In the event, cost factors led to the choice of a residential rural campus in converted buildings when, in 1976, Buckingham opened for business with just 46 students.

Initial ideals had to adapt to the market when the Council for National Academic Awards refused to validate degrees, meaning that early graduates were awarded only "licences".

A crucial development came when the Law Society and Bar Council gave professional exemptions to holders of Buckingham "licences" in law.

Law soon proved a popular option since there was excess demand across the whole sector, and the combination of long terms and two-year degrees with high fees suited some mature students or those who had been made redundant and wanted to upgrade their skills during recessionary times.

It also led to an unexpected influx of applications from overseas, particularly the Commonwealth, where Buckingham's fee structure made it comparatively competitive with other British universities.

The success of Buckingham's law degrees set a more general pattern in which stress was put on "professional" courses in areas such as accountancy and business, with limited provision of more traditional non-vocational academic subjects.

About half of the students now come from outside the European Union.

Initial expansion gave way to stagnation in 1994-95 and then decline in 1996-2000 owing to exchange rates and the growth of the state sector.

A low point was reached in 2001, with student numbers down to about 600. But since the arrival that year of the current vice-chancellor, Terence Kealey, there has been a notable revival.

He has been responsible for the creation of a medical school, a school of engineering, a course in automotive engineering management (partly to cater to the needs of nearby Silverstone) and a programme in business enterprise offering students a chance to run their own businesses.

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There are now about 90 full-time academics (and 40 part-timers) serving a student body of around 1,000.