Speaking at a fringe event hosted by Million+ at the Liberal Democrat conference in Brighton, Mr Cable looked back at the battlegrounds in higher education since the coalition came to power.

He said that the Department for Business and Innovation and Skills had been obliged to deal with a 25 per cent cut to its budget, "which is what my predecessors [the Labour party] were planning anyway".

Questioned about the differences between the new funding system and a graduate tax, Mr Cable said: "The reason it happened the way it did was that when Lord Browne did his report he made a trenchant attack on what has subsequently been called a pure graduate tax."

The government "didn't buy" that version, he said. But he added: "A form of graduate tax is effectively what we introduced and I regret that, from a presentation sense, we didn't say that from the outset. It changed the dynamic of the debate in an unhelpful way. That was a mistake, but we are where we are. Increasingly we should try to use that language because it is more accurate."

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But Liam Burns, president of the National Union of Students, sitting alongside Mr Cable on the panel, immediately countered: "I just think that's wrong."

Mr Burns said the "up-front sticker price" attached to courses under the present system of tuition fees meant it was "nothing like a graduate tax".

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The present system is a "weird pseudo-financial product that no other generation has ever been subjected to", Mr Burns argued.

Another factor that meant the present system cannot be described as a graduate tax is that the fees are variable, he added. And these fees "have absolutely no bearing" on what will be repaid other than for the highest earning graduates, because most will not repay in full, Mr Burns said.

This meant students could be "conned into thinking 'I can't afford the ?9k institution so I'll go for the cheaper ?6k'".

Mr Burns and Mr Cable also clashed over the shortfall in the number of students entering higher education in 2012.

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Mr Cable said that while there had been an impact on undergraduate demand, "you have to take it in the context of universities being heavily over-subscribed".

But Mr Burns replied: "There's 21,000 clearing [places] still left, that's not oversubscribed."

john.morgan@tsleducation.com