It is 3.55pm on a dark winter's afternoon, but the philosophy seminar on "Radical democracy and Rousseau" shows no sign of flagging.

Eager, earnest students are still desperate to make their final points before the hour is up, awaiting that split-second pause that will let them jump back into the debate.

Close your eyes and you might well think you were listening to a typical undergraduate tutorial, complete with idealistic, left-wing students keen to challenge their classmates, the lecturer and society in general - that is until you hear the sound of the No 76 bus to Waterloo thunder past just a few yards away.

This is actually Tent City University, the centrepiece of the Occupy London camp outside St Paul's Cathedral, a "pop-up" seat of learning spinning off from the anti-capitalist protest movement.

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The flimsy plastic sides of the makeshift marquee are the only thing that separates visitors from the freezing elements and the din of central London traffic, but Tent City University has become one of the camp's big success stories.

Thousands of people have sat down here to listen to academics, writers and political activists hold forth on a variety of subjects since the camp was set up on 15 October last year.

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Today, an unlikely mix of anti-capitalists, American tourists, smartly dressed Londoners and shoppers perch on the university's battered old sofas and tatty floor cushions ready to learn about the 18th- century Swiss philosopher.

"It's a place to exchange ideas and think creatively about what life should be about," explains Joan Safran, a former philosophy lecturer at City University London who leads the lively discussion group.

"Universities are places to think and then test your ideas with other people, and so is this place.

"I've been politically left-leaning all my life, so I was happy to support this project."

Academics have been eager to volunteer their time to lead lessons, with dozens offering to host talks, panel discussions and public debates.

"They are frustrated with what is happening at our universities," explains James Sevitt, a Canadian documentary-maker who is one of the centre's organisers.

"However, they want to salvage what they love about them - the questioning of knowledge, discussion, intellectual freedom.

"Here, they don't have to deal with the bureaucracy or market forces that you find in universities nowadays.

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"Attendance varies from 10 or so people to the hundreds who turned out to see Jesse Jackson speak in December.

"We had more than 100 turn out to see economist Ha-Joon Chang (a reader in economics at the University of Cambridge) talk about the things they don't tell you about capitalism, while we've had about the same number to see [the journalist] Polly Toynbee.

"The sessions can be about anything, though they normally relate to what we're doing here.

"But not always - shamanic drumming wasn't my personal favourite, but we had it."

Other academics to have addressed Tent City University include Gabriel Palma, a senior lecturer at Cambridge, Sabina Alkire, director of the Oxford Poverty and Human Development Initiative at the University of Oxford, and Ken Jones, professor of educational studies at Goldsmiths, University of London.

But does it add up to anything more than a forum for debate, a glorified talking shop? And, for all its lively debate, is there anything at Tent City University that could eventually resemble a structured course of learning found at a traditional university?

Work is well under way to progress the scope of the initiative beyond one-off talks. Although vocational courses in motorcycle and bike repair have been mentioned as future study programmes, a 30-strong "non-hierarchical" organising committee is discussing whether courses should have reading lists, exams or assessment through essays.

At Tent City University's sister scheme, the Bank of Ideas, housed in an empty office block owned by the Swiss bank UBS off Liverpool Street, the learning programmes are more advanced.

Here, several courses of evening classes lasting 10 weeks are already up and running, alongside stand-alone talks spanning everything from the philosophy of art to modern clown studies and how to start a squat.

Led by "Bill", who asks not to be identified, a recent University of London linguistics PhD graduate, the session on the rise of US drone attacks in Afghanistan and Pakistan is a promising start to a course - packed with detailed military history, statistics and political insight.

Admittedly, it's hard to concentrate on US foreign policy when squatters keep tramping through the tutorial room - everyone from dreadlocked hippies to wailing toddlers drift through the communal office space - but the handful of listeners seem enthused.

"We're not trying to junk the existing university system or replace it," explains Bill.

"For one thing, it has produced some very good thinkers who play a vital role in society.

"But I would say that many academics have been corrupted by the incentives on offer, which has made them forget the purpose of a university.

"Teaching is often too much about getting graduates a job, while researchers are under pressure to turn out research papers.

"The Bank of Ideas is very accessible and people want to learn. Getting a discussion started at a normal university is often like pulling teeth, but that's certainly not true here."

"Alternative universities" also feature at Occupy camps in New York, Dublin and Copenhagen. However, many expect these informal institutions to be short-lived.

"These alternative universities are an expression of a very noble and important reforming movement...but I don't think they will have any staying power," says Terence Kealey, vice-chancellor of the University of Buckingham, Britain's only established private university.

"Capitalism is facing a crisis. It's completely appropriate that we are questioning why bankers are paying themselves so much.

"We should have a dialogue about capitalism and whether the [City of London's] 'Big Bang' [in 1986] and the huge deregulation of the system under Thatcher have gone too far. Capitalism needs to be saved from itself.

"But these spontaneous universities will last only as long as the tent city itself."

Kealey says that spontaneity has always played a role in higher education. "The travelling masters of medieval times were involved in spontaneous teaching," he explains.

"Before Abelard, you could argue that Socrates created a university [on his travels].

"The very first university at Bologna was founded by a group of law students, while Oxford was started by academics disillusioned with Paris.

"But very quickly these universities needed licences from bishops, princes or kings to continue. The definition of a university is 'an institution in higher education recognised by a sovereign'. If you don't have a charter, you're not a university."

Kealey likens the current alternative universities to the underground education movement in Communist-ruled Czechoslovakia before the fall of the Iron Curtain.

Supported by the prominent Western European philosophers Roger Scruton, Jacques Derrida and Anthony Kenny, who were all arrested on visits to Prague in the 1980s, secret networks of educators held seminars in living rooms and kitchens.

This movement echoed the "flying universities" of Russian-occupied Poland that were started in the late 1800s, and which trained thousands of men and women, including Marie Curie, the Nobel prize-winning chemist and physicist.

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Under Nazi occupation, underground colleges were re-formed when Polish universities were closed. Pope John Paul II was first trained at a clandestine underground seminary.

"Whenever there is a sense that authority has created too many obstacles to education, people create their own universities," says Kealey.

While today's alternative universities in England are not the result of oppression, a few of them have been set up in response to what some fear will be a barrier to higher education: the new higher tuition fees being introduced this autumn. Several put the issue of free education at the heart of their mission.

Established in May 2011 as a "not-for-profit, non-hierarchical, unincorporated co-operative", the Social Science Centre in Lincoln offers a fully developed model of a free alternative university.

Starting this autumn, the centre intends to teach 20 students, whose work will be graded to university level by volunteer lecturers employed at other higher education institutions.

These academics - there are currently 30 signed up - will also contribute the equivalent of one hour's net pay a month (?14 a month for a lecturer earning ?40,000 a year) to cover the centre's running costs, estimated at ?7,200 a year.

Students will study part-time for up to six years to gain a certificate that centre organisers say will be the equivalent of a degree. A master's course will take up to four years and a PhD up to eight. Students of the centre will be given reader cards that allow them to access the University of Lincoln's library.

Learners will be invited to collaborate with academics on research papers and to help design the courses in the spirit of mutual learning between teachers and students.

"It's an alternative form of higher education for students unwilling to take on the debt associated with a degree," explains Mike Neary, dean of teaching and learning at the University of Lincoln.

"It offers a very small provision, but the model could be taken up in other parts of the UK."

He hopes the centre will "gain a reputation for excellence", which could enable its students to progress to mainstream institutions under the university's accredited prior learning scheme.

Other initiatives include the Really Open University, a Leeds-based project that seeks "the creation of a free and empowering education system", instead of "elite institutions benefiting a privileged minority".

Started in late 2009, the pressure group runs a rolling programme of talks on counter-cultural issues, local history and radical cinema, as well as publishing newsletters and journals on higher education.

There is also the Dublin-based Provisional University, which draws inspiration from the outdoor "hedge schools" that started in 18th-century rural Ireland after Catholic schools were outlawed from 1723 to 1782.

A supporter of Occupy, the Provisional University seeks to restore "autonomous education" and break free from the "university as bureaucracy".

Similar grass-roots organisations committed to free education have emerged across the world.

Self-organising education movements led by academics can be found in Cairo, Athens, Jerusalem and Los Angeles, says Irit Rogoff, professor of visual cultures at Goldsmiths, who is working on a research project examining the centrality of self-education projects to recent protest movements.

She traces the rise of alternative universities back to radical art schools, citing the United Nations Plaza in Berlin (in 2006-07) and the Night School in New York (in 2008-09), as forerunners to today's organisations.

"The art world, working in conjunction with activist networks, set up new models of education [and] new public sphere forums," Rogoff explains.

"These have, in turn, been taken up within revolutionary protest movements and civic occupations.

"Of particular interest is this new model of education, whose delivery is a radical departure from university courses with their curriculum and top-down perception of knowledge."

Ignoring these hierarchies has helped to "shift the discourse from the cognitive capitalist demands for 'transferable knowledge' to modes of self-education and transformation", she argues.

Among the most sustained of these was the Copenhagen Free University, which was wound down in 2007 after six years of challenging the "financialisation of our brains, our nervous systems, our subjectivity, our desires, our selves", according to its organisers. They claimed that the idea of the self-organised university had become so widespread that there was no need for such a fixed base.

Will these movements ever rival the conventional university?

Rogoff believes this is unlikely. Rather, the primary role of alternative universities is to act as a wake-up call for mainstream higher education. She hopes that an understanding of alternative universities will help conventional universities, "which are feeling beleaguered and less and less relevant as sites of innovative or urgent thinking", recognise "how they might renew themselves".

Reading the revolution: Help yourself to a book - Cicero would want you to have it

"A home without books is like a body without a soul". Those words are scrawled on a piece of cardboard that is pinned to an inside wall of Tent City University.

The quote, attributed to the Roman statesman Cicero, captures the importance of the free library to the free education centre.

Since 15 October, the library has received about 10,000 books from well-wishers, according to organiser Nathan Cravens.

The library is "very popular", observes the -year-old Texan, and attracts a variety of users, including tourists, City workers and local residents, who are free to take away the books.

Titles on offer include marketing dictionaries, encyclopedias, self-help books, a first-aid manual and modern classics such as D.H. Lawrence's The Rainbow.

Two signed copies of Alan Bennett's The History Boys and A Life Like Other People's also made their way on to the library's bookshelves after the playwright and author visited the tent in November, and both were quickly snapped up.

Cravens believes that, in future, students of Tent City University will sit exams in the tent and make motorbikes from scratch under the guidance of mechanics.

Others plan to give workshops at schools and colleges to explain the protest's purpose.

Tent City University is "the best thing about Occupy", says Jack Dean, a post-production technician at a Soho film company who is manning the help desk during a week off work.

"I've had some of the most interesting and challenging conversations of my life in there."

One visitor to the library is Mike Faulkner, a former history lecturer at Barnet and Southgate College.

He offers to hold a talk about the life of the black singer, actor and civil rights activist Paul Robeson, who sang to more than 5,000 people gathered on the steps of St Paul's in 1958.

If he were still alive, the champion of social justice would probably be back in London to support the Occupy cause, Faulkner contends.

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"There is a mood of anger and a determination among a growing minority to resist," he says. "It is this that has prompted so many academics and others to publicly demonstrate their support."