This week, we invited two heavyweights of UK higher education policy to our London headquarters to take part in a video debate.

In the red corner was Andrew Adonis, Labour peer, former education minister and architect of the ?3,000 tuition fees system; and in the blue corner, David Willetts, Conservative peer, former universities and science minister and the man who introduced the ?9,000 tuition fees system.

We expected a fiery exchange ¨C particularly given that Lord Adonis has been a fierce critic of the tuition fee system established by Lord Willetts, and in return, Willetts has poo-pooed Adonis¡¯ calls for fees to go.

The discussion did not disappoint. Adonis got straight down to the business of how universities should go about taking the initiative on fees, calling on them to cut tuition costs ¡°by about ?1,000 a year for the next few years to diffuse the sense of crisis over the system¡± and ¡°get students on their side¡±.

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¡°If they don¡¯t do that, I think what will happen ¨C as is happening in the United States at the moment with states abolishing fees and has happened across continental Europe and may well happen in New Zealand too ¨C is that politicians will abolish them,¡± he concluded.

Willetts hit back with a point on which it appeared to me he hoped to find some common ground with Adonis. The ?9,000 system, he said, ¡°ensures they have a well-funded education without number controls, and if we bring back public spending on the scale Andrew wants it, we¡¯ll have number controls back¡±.?

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He appeared to be of the opinion that surely Adonis would agree that removing number controls was a good thing. Indeed, he described the removal of caps as ¡°a great prize¡±.

Adonis, however, was having none of it in what was an increasingly confrontational discussion. ¡°We¡¯ll have number controls back anyway ¨C it¡¯s only a matter of time, and I think a short period of time,¡± he said.

The reason? He says the Treasury agreed to Willetts¡¯ request to lift the cap only?because it would get ¡°a substantial real rate of interest¡± back on loans as part of the ¡°deal¡±. Interest on repayments is currently 6.1 per cent, something Adonis says is so politically toxic that it will need to be scrapped before the next general election.

¡°In return for scrapping that real rate of interest [the Treasury] will absolutely go back to number controls. So that will happen either next year or the year after, whenever the interest rate comes down.¡±

It is worth noting that Willetts dismissed this (in no uncertain terms) as ¡°incorrect from every point of view¡±. He did, however, concede that there was at least one problem ¨C or ¡°issue¡±, as he termed it ¨C with the current system.

¡°I think there is an issue about graduates from lower income backgrounds leaving university with more debt than graduates from more affluent backgrounds,¡± Willetts said. It was refreshing to hear him acknowledge this ¨C the problem was highlighted by the Institute for Fiscal Studies as regressive and a key problem in the current system.

Another issue that prompted some intense disagreement was vice-chancellor pay. It is not surprising ¨C Adonis has made his disdain for senior management pay levels very public indeed through his relentless tweeting and high-profile articles on the issue. Times Higher Education has long been the principal exposer of vice-chancellors¡¯ salary levels through its annual VC pay survey, and continued analysis of the issue.

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In the debate, Adonis claimed that cuts to senior pay could generate millions of pounds for every university in the country.

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¡°Senior management teams of universities are bloated and massively overpaid,¡± he said, ¡°and if you cut that back by about half, which is what would happen in any other efficient public sector organisation, and reduce the salary bill, in each institution that would give you between ?5 million and ?10 million to play with.¡±

It seems so simple, right? ¡°You could cut the fees substantially without affecting the quality of education,¡± he posited.

Willetts?was not impressed, lambasting ¡°the idea that somehow the money you [could] save on [salaries] is anything like matching the scale of the loss of funding¡­which Andrew is proposing¡± through his suggested fee reforms.

Perhaps the biggest row erupted over the concept of a tuition fee cartel. Adonis believes that the reason the vast vast majority of universities have set their fee levels at the maximum possible level is because they colluded on price.

¡°It¡¯s manifestly a cartel,¡± he said when given the opportunity to clarify his position by chair John Morgan. ¡°You can have your own view about whether universities engaged in a cartel,¡± Adonis continued. ¡°My own view is that they did¡­we all know how the universities work ¨C they all meet in Universities UK the whole time, they exchange notes all the time, a whole lot of private conversations take place.¡±

Willetts, following Morgan¡¯s lead, explained his belief that the ¡°generous¡± repayment model means that ¡°because quite rightly students don¡¯t pay up front, that the distinction between ?7,500 or ?8,500 is not what matters¡±. The universities, Morgan said, were simply ¡°behaving rationally¡± by gravitating towards the highest fee levels.

Adonis hit back again. ¡°[Willetts¡¯] reform only passed because of the assurances he gave to Parliament that fees would be related to the value to the gradates, that they would not all go up to ?9,250¡­If he¡¯d been honest about what he was doing, his reform would not have passed through and we wouldn¡¯t be in this mess.¡±

The two lords also had their say on two-year degrees, the ¡°windfall¡± that universities received as a result of increased fees, and what the priorities for Labour leader Jeremy Corbyn should be at the next election. Watch the video above to view the debate in in full. There¡¯s also a full transcript here.?

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Chris Parr is digital and communities?editor at Times Higher Education.