The heads the elite Russell Group of universities, including Oxford, Cambridge, Imperial and University College London, are calling for a rise in tuition fees.
They want to abolish the £3,225 a year limit on fees and allow universities to charge what they want. This would mean a system where top universities charge prices that ordinary students cannot afford. Fees could rise to as much as £20,000.
The review of student finance is currently being run by Lord Browne, the former head of oil giant BP.