The government could be forced to spend almost £1bn more than expected over the next four years to cover the cost of tuition fees, as a growing number of universities set out plans to charge the maximum of £9,000 a year.

From autumn next year, universities will be allowed to almost treble the amount they now charge, as part of a reform of the funding of higher education. The initial charge is borne by the government, which pays the fee for each student in the form of a loan before recovering its money once the student has graduated and finds a job that pays more than £21,000.

Critics fear that the government will claw back the initial outlay from other higher education spending, potentially leading to fewer university places or cuts in research budgets.

David Willetts, the universities minister, had anticipated that a market would develop, with institutions charging a wide range of fees, but a picture is emerging of the majority of institutions charging the top rate. Of the 16 universities that have so far stated how much they intend to charge, 13 want the maximum – University College London, Birmingham and Lancaster being the latest to do so.

Willetts predicted that the average across the whole of higher education would be £7,500. It now looks much higher, but the Treasury has used the £7,500 average to determine how much universities should receive for research, teaching and building grants, among other things. Figures from the House of Commons library show that if the average is £8,600, the government will have to spend £960m more in the next four years. If it is only slightly higher, at £7,900, it is £340m extra. But if the average is £8,900, the government will have to pay out an extra £1.23bn.

The funds could be deducted from universities' budgets and could mean fewer places on degree courses or a cut to the research or teaching grant. A total of £940m has already been cut from English universities' budgets for teaching, research and site renovation for the next academic year, a 12.6% reduction. However, last week's budget awarded an extra £100m to research.

Gareth Thomas, the shadow universities minister, said either universities would have their funds cut or the government would have to reconsider altogether. He said: "The government repeatedly promised that fees over £6,000 would be the exception, but it is increasingly clear that they are powerless to stop most universities charging closer to £9,000. This will push up average fees beyond the £7,500 estimate on which the government's spending plans are based, requiring deeper cuts elsewhere in the higher education budget."

Other universities seeking the £9,000 maximum are Oxford, Cambridge, Imperial College London, Exeter, Essex, Aston, Manchester, Warwick and Durham. St Mary's University College, Twickenham has said it plans to charge £8,000.

Universities that charge more than £6,000 must set out a plan, or access agreement, to widen their pool of students beyond white, middle-class teenagers, and this must be approved as adequate by the government's access watchdog, the Office for Fair Access. Institutions have until 19 April to submit their access agreements to Offa, which will give its verdicts in July.