"The vast majority" of universities are not discriminating against applicants from private schools, according to a leading independent school head teacher.
Bristol has been accused of turning down good students
Graham Able, chair of the Headmasters' and Headmistresses' Conference, said: "In most departments even in the other ones there is no noticeable discrimination whatsoever."
Some schools have complained that their students are being refused places simply because they are from the independent sector.
Mr Able, head of Dulwich College in south London, said there might be problems with some courses.
He mentioned Bristol as being "in the firing line", though he acknowledged its complaint that it is heavily over-subscribed.
Speaking on the BBC Radio 4 Today programme, Mr Able said it was possible to widen the base of university admissions to people from less advantaged backgrounds without discriminating unfairly.
"But it does require very, very careful selection.
"It requires interviewing as well as A-levels, and you can spot people who are extremely talented who may miss out on a grade - we would not in any way criticise any university for accepting those, Oxford and Cambridge have done it very well for some years."
Bristol has said it does turn down well-qualified applicants because it does not have enough places for all those who apply, and does not have the resources to interview everyone.
It is more likely to look twice at people whose schools do not have a record of academic excellence because they might have the greater potential.
Independent school pupils in the UK account for about 7% of the secondary school population but about 14% of university undergraduates.
Their representation in some universities is far higher.
At Bristol, for example, 63.4% of the applicants for 2002 entry were from state schools and 29.8% from independents (the balance being mature applicants and others).
The university accepted just under 61% from state schools and 33.6% from independents.
On the same programme, Liberal Democrat higher education spokesman David Rendel said the bias had been the other way round.
"What's been happening up till now is that there's huge discrimination going on, in favour of those that go to independent schools."
Universities had chosen their students almost entirely on the basis of their predicted A-level results.
"The independent schools are very good at knowing what the A-level examiners are looking for and making sure that their pupils get better A-level grades."
Mr Able said he expected that a lot of boys would achieve better A-level grades at his school than at a less good school - state or private.
"What I am against is quotas and benchmarks which have no place in university admission whatsoever."
Merit and potential
What has refuelled the debate is the government's decision to set up an "access regulator" to decide whether universities will be able to charge higher tuition fees from 2006, on the basis of their plans to widen access to their courses.
It has yet to be decided how this will operate.
But the Conservatives' education spokesman, Damian Green, has said his party would abolish this "admissions czar".
"Academic merit and potential should be the only factors in deciding university admissions," he said.
"Telling students that their exam grades don't matter because they went to the wrong type of school, or because their parents were too well-educated, is a terrible position for universities to take."
He said the problem of getting children from disadvantaged backgrounds to apply to university should be solved in the schools, by giving every child the chance of an excellent education.