Some universities are considering taking undergraduates to the small claims court if the final instalments are not forthcoming and non-payers could be thrown off their courses.
The overdue payments represent 10 per cent of the pounds 150m collected by universities in the first year of the introduction of the new system of fees.
The survey, carried out by the Committee of Vice-Chancellors and Principals (CVCP), found some evidence that universities were finding it harder to collect other charges, like accommodation fees, and they warned that overdue fees from this year may have "knock-on" effects for next year's fees.
But universities said the outstanding debt was smaller than expected and insisted the first year of fees had proved a success. The survey was carried out in mid-June and vice-chancellors insist thatdebt is likely to fall by the autumn when final fee instalments have been paid.
Universities are expecting to write off some fees and are warning that ministers will be asked for extra funds if bad debts exceed the pounds 20m set aside to cover the scheme.
Baroness Diana Warwick, chief executive of the CVCP, said: "It is reassuring that the vast majority of fees have been paid in this first year and that there is no evidence of systematic non-payment.
"However, we are concerned that some students still owe their fees or part of them. The scheme is fair. All fees are means-tested and a third of students, those from poorer backgrounds, are charged no fee at all, so students should be able to pay."
Each university is responsible for collecting up to pounds 1,025 from each student, although most have allowed students to pay in instalments. Only a handful have refused to pay, despite a protest by Oxford first-year students last year.
A spokesman for the National Union of Students, which opposes fees, urged universities to treat those in arrears with sympathy. He said: "This means there are a lot of people of have tried to pay their fees and we are calling on universities to listen to the Government's guidelines and be as flexible as possible.
"We have always argued that there would be a lot of people having difficulty paying their fees and these people will need universities' help to work out payment schemes."