Ministers have suffered a major blow to their tuition-fee reforms after the government's access watchdog revealed that all universities intend to charge at least £6,000 a year.

The Office for Fair Access (Offa) announced that every one of the 123 universities and university colleges in England intend to charge £6,000 or more to full-time undergraduates from autumn 2012. A further 17 further-education colleges – out of 124 – want to charge fees of more than £6,000. Universities had until midnight on Tuesday to submit their plans to the watchdog.

Offa would not say how many of the institutions want to charge the maximum fee of £9,000. However, research by the Guardian has revealed that almost three-quarters of English universities and university colleges intend to charge this amount for at least some of their courses.

The figures will come as an embarrassment to David Willetts, the universities minister, who predicted that universities would charge different levels of fees and that the average would be £7,500. He later revised that to £7,500-£8,000.

The Guardian's figures show the average fee of those that have made their plans public currently stands at £8,629.73. Some 49 of the 73 universities intend to charge a flat rate of £9,000. Some 56 institutions intend to charge £9,000 for at least some of its courses.

MPs voted in December to raise tuition fees for full-time undergraduates from £3,350 a year to £6,000 in 2012 and up to £9,000 in "exceptional cases".

But new and old universities have announced plans to charge £9,000. In the last few days Bradford, Bristol and Hull universities have said they want to charge the maximum. Oxford Brookes and University of East London – neither of which are in the top 40 universities according to the Guardian's university league table – intend to charge a flat-rate of £9,000.

The University Centre at Blackburn College has decided to set its fees at £7,000.

Some 73 out of 123 universities or university colleges have now publicly declared their fees. Some 50 others have given their proposals to Offa privately.

The Treasury is faced with a funding black hole because the initial cost of students' fees is borne by the government. It pays the fee for each student in the form of a loan. The government then recovers its money once a student has graduated and is earning more than £21,000.

Labour said on Tuesday that one way for the government to claw back the higher upfront cost would be to cut student numbers. Ed Miliband, the leader of the Labour party, warned that at least 10% of university places for undergraduates would have to be cut to fund the coalition's "unravelling" tuition fee reforms.

This is the equivalent of removing 36,000 full-time places each year.

Universities that want to charge more than £6,000 had to tell Offa what their targets were to widen their pool of students beyond white middle-class teenagers. These must be agreed by the watchdog. Offa has the power to tell universities that they cannot charge more than £6,000 and will be able to tell institutions next year that they must lower their fees because they have not fulfilled their targets. The government has recommended that universities spend £1,000 out of every £9,000 received in fees on support for students.

The watchdog will announce in July whether it has accepted each university's plans for 2012.

Some universities, such as Coventry, intend to charge variable fees based on the cost of delivering their courses. Coventry wants to charge £7,500 for classroom-based degrees; £7,900 for studio and field trip-based degrees; £8,300 for lab-based degrees and £9,000 for specialist degrees such as engineering, fashion and automotive and transport design.

Meanwhile, it has emerged that overseas universities are redoubling their efforts to recruit English students to their universities.

Paul Loftus, managing director of i-studentgroup, which helps universities in the UK, Australia, Canada, the US and New Zealand with their recruitment, said foreign universities were targeting the UK. "If overseas universities haven't started lifting their recruitment efforts to try to get British students, they are now."

Loftus said more British students than in the past were considering going abroad for university, in part because of higher fees. "Although the Australian dollar is strong, many British teenagers are enrolling on courses in Australia, Canada and New Zealand in particular."

Aaron Porter, the NUS president, predicted that 10% of university applicants would be put off studying for a degree because of the higher fees.

"Sadly we are hearing that some students are deciding not to apply already. We hope this sends out an urgent message to the government that their tuition fee policy is in disarray."

The number of students who want to travel or work abroad for a year before going to university has dropped by almost half, The Times has reported.