The Labour Government and Conservative Opposition were accused of "conspiring" to keep fees off the agenda until after the general election following the launch of the long-awaited fees review this week.
The review will be led by Lord Browne of Madingley, the former head of BP, and will examine fees and financial support for full- and part-time students and for postgraduates. It is expected to report by autumn next year.
However, it was denounced by Stephen Williams, the Liberal Democrats' higher education spokesman, as "nothing but a conspiracy between Labour and the Tories designed to keep plans to hike up tuition fees off the agenda until after the general election".
The announcement of the review came as the initial findings of a poll by Times Higher Education revealed the range of opinion on the issue among vice-chancellors - speaking on condition of anonymity - and within mission groups.
Most vice-chancellors believe the cap should be lifted, with the suggested figure ranging from £4,000 to £7,000, while a significant number argue there should be no cap.
"The cap on fees should be lifted to allow full market forces to come to bear," said one.
Another vice-chancellor agreed: "We cannot avoid this if UK higher education is to remain world-class."
A third claimed that universities in the Russell Group of large research-intensive institutions were "clamouring" for a fee of £7,000, which was not affordable.
Several said they would prefer fees not to rise, but recognised that it was an "inevitability", and therefore favoured a cap of £5,000.
But not all university heads believe a rise in fees is a certainty.
One said the Government might be deterred by public opinion - a recent poll found that only 12 per cent of the public think the review should consider increasing fees - and by the potential increase in public sector borrowing. Others favour a continuation of the status quo or a move to graduate tax.
Responding to news of the review, the Russell Group argued that an increase in fees would be "one of the most effective" options, while Million+, which represents new universities, chose to highlight the difficulties faced by part-time students.
Sir David Watson, co-director of the Centre for Higher Education Studies at the Institute of Education, University of London, said that, as long as fees are paid in advance by the Government, with the intention of later recovery, "there is no real room for manoeuvre, with either the cap or the official bursary position".
The review will examine the "balance of contributions" by taxpayers, students, graduates and employers.
Issues covered will include widening participation, fair access, bursaries, the diversity of models of learning, affordability and value for money.
They will be joined by Sir Michael Barber, head of management consulting firm McKinsey's Global Education Practice; Diane Coyle, who runs the consultancy Enlightenment Economics; Rajay Naik, commissioner on the Standing Commission on Carers at the Department of Health; and Peter Sands, group chief executive of the Standard Chartered bank.
Any changes will be implemented in 2011-12, at the earliest.
Lord Browne, the former head of BP, will head the fees review. He studied physics at the University of Cambridge, and is a fellow of the Royal Society and president of the Royal Academy of Engineering. He joined the oil company as a university apprentice in 1966, rising to become its head almost three decades later.
Lord Browne resigned from BP in 2007 after it emerged he had lied to the High Court when attempting to obtain an injunction to block a kiss-and-tell story by a former lover.