Speaking to The Independent, Professor A C Grayling said major institutions such as Oxbridge may even be forced to drop out of the state funding system altogether and go private to keep their top rankings.

Professor Grayling, who is charging students £18,000 a year for a place at his New College of the Humanities, said a fee cap of £9,000 a year was "unsustainable" for universities that want to attract the best students.

Ministers are believed to be reluctant to propose a new rise in tuition fees before the next general election, which may force leading universities to act. They also may take matters into their own hands if Labour wins the election, as the party is committed to reducing fees to £6,000 a year.

Last night, Cambridge said it was "currently remaining within the state system and charging the maximum fee of £9,000 a year". A spokesman added: "Professor Grayling is speaking for himself." Oxford declined to comment. Ministers are believed to be reluctant to propose a new rise in tuition fees before the next general election, which may force leading universities to act. They also may take matters into their own hands if Labour wins the election, as the party is committed to reducing fees to £6,000 a year.

Speaking after his appearance at the Hay Festival, Professor Grayling said: "Oxbridge have already been looking at becoming independent and the reason is the £9,000 cap. It's the Tesco thing of pricing something at £9.99 rather than £10 or £15. Two months ago Cambridge published costings on how much it costs to teach humanities students, and they found it to be £17,500 a year. If you look at all the comparators – up to £30,000 for private schools, or overseas students whom we charge £15,000 to £40,000 – that is the true cost of education. Major institutions are going to find it unsustainable to keep charging these fees."

The creation of the New College of the Humanities last year provoked intense debate about whether higher education was destined to become prohibitively expensive. But Professor Grayling said this need not be the case. "I'm sorry there will be increases, but that is not inconsistent with what I am doing," he said. "People think I've betrayed my leftie principles, but I want to see strong public sector universities and I think society should invest in education at all levels, including higher education. It is a social good. I'm trying to be a realist. If we have given up the idea of providing a stellar education from the public purse, we have to look for an alternative."

Professor Grayling's college, which has an impressive roster of lecturers including the historian Niall Ferguson and writer Howard Jacobson, set its fees at £18,000 last year. He believes that copying the American model of private universities with endowments is the route that top universities in Britain should be going down at if they want to keep education open to all.

"My own ambition is to raise an endowment, like Harvard's $20m, to support the students," he said. "Harvard, Stanford and Princeton charge £50,000 but because of endowments they can offer proper support to many of their students. There's a possibility that, if we can create such an endowment, we would end up running the only higher education institution that will be able to educate all its students for free."