Ministers underestimated how many universities would charge £9,000 fees – and now face huge bill to fund student loans

Tough quotas on student numbers may have to be introduced to avoid the creation of a spending black hole under plans to raise tuition fees at English universities to a maximum of £9,000, a powerful committee of MPs has warned.

Ministers underestimated how many universities would charge the maximum fee and now face an annual bill to fund the interest-free student loans that is "several hundred million pounds" higher than anticipated, the Public Accounts Committee (PAC) reports.

The current balance of outstanding loans – £24bn – is expected to rise to £70bn by 2015-16, the report says.

Margaret Hodge, the chair of the committee, said: "At present, more universities intend to charge higher fees than the department had expected. If the universities' plans to widen participation are approved by the Office for Fair Access, this will leave a substantial funding gap which will either require further cuts in higher education or further resources from the Treasury."

Whitehall sources told the Guardian they would not know the true cost of the policy until students had turned up at freshers' week in 2012.

Reducing student numbers below the current cap would prove deeply unpopular after several years of increasing demand and an annual row over the competition for university places.

While some students will forgo loans and universities will subsidise some of the fees with bursaries, ministers will still have to consider other options "which might range from finding more money through to reducing places available", the PAC report says.

Figures compiled by the Guardian reveal that as of Monday, 105 universities had declared the fee they will charge, with an average of £8,765. The government modelled its plans on an average fee of £7,500. The Office for Fair Access is vetting universities' fee plans. They will announce on 11 July which have been agreed.

A Whitehall source said uncertainty over the costs was inevitable given the number of variables but insisted that they were confident that the figures they had used were the best projection.

Whitehall sources indicated on Monday that students at the New College of the Humanities – a new private university being set up by high-profile academics including AC Grayling – would not be entitled to government-backed student loans because its £18,000-a-year fees break the £9,000 cap.

The university's backers have said they expected students to be eligible for loans of up to £6,000 from next year in line with other private universities. They are also seeking commercial loans.

The forthcoming white paper on higher education is expected to set boundaries of a "level playing field" between traditional institutions and new private providers. Only students at universities charging under the £9,000 cap are expected to be eligible for state-backed finance.

Ministers are expected to pave the way for students educated privately to borrow up to £9,000. However, private universities charging fees above £6,000 are also expected to become subject to government requirements on widening access to students from poorer backgrounds.

A growing number of universities are warning of uncertainty over the policy. Nicola Dandridge, chief executive of umbrella group for higher education, Universities UK, said: "While it is quite clear that changes are ahead, there is still a great deal of uncertainty as to the level of student demand and for which courses, and the extent to which students will take out student loans. The final cost of the new funding system to the government is therefore far from clear."

But the uncertainty is compounded by predictions that applications could collapse when students are faced with higher fees, putting some less popular institutions in financial jeopardy.

The PAC calls for clarification about what the government will do when universities are in danger.

Meanwhile Oxford University is poised to take an unprecedented vote of no confidence in the higher education minister, David Willetts, on Tuesday in the most aggressive act of the university against a government since its dons vetoed an honorary degree for Margaret Thatcher.

Oxford dons will vote on a resolution that says: "Congregation instructs council to communicate to government that the University of Oxford has no confidence in the policies of the minister for higher education."

Cambridge, Goldsmiths and Warwick are to embark on similar exercises. There is fury in parts of the academic community about the hikes in fees – but also about funding cuts, particularly to the arts.

Sally Hunt, general secretary of the University and College Union, called on every university to hold a vote of no confidence claiming that the plans were in "disarray".

• This article was amended on 7th June 2011. It originally stated that the Oxford vote of no confidence in David Willetts was on Monday. It is in fact scheduled to take place on Tuesday.