Bristol has been accused of turning down good students
Head teachers at independent schools are to discourage sixth-formers from applying to Bristol because of claims the university discriminates against private school pupils.
A group which represents the heads of public schools says it is advising its members not to encourage children to apply for Bristol.
The Headmasters' and Headmistresses' Conference (HMC) and the Girls' Schools Association (GSA) are stopping short of a boycott, because they say their members cannot stop children from applying where they want to.
But their advice signals an attempt to increase pressure on universities as they seek to widen access to children from poorer families.
A statement from the organisations said: "All the evidence we have is that most selecting universities are continuing to adopt admissions procedures which are fair and appropriate to the high demand for their courses.
"Bristol, however, has been very public about a policy which unfairly discriminates against applicants from good schools, whether independent or state.
"A high degree of concern has emerged from member schools this year about apparently arbitrary rejection of well-qualified candidates."
The organisations want their members not to encourage pupils to apply to Bristol "for the time being".
They say they want reassurance from Bristol that its procedures are "fully documented, fair, objective, transparent and consistently applied".
Bristol has denied allegations that it positively discriminates against pupils from private schools or top state schools in favour of children from less-advantaged backgrounds.
It says it is heavily over-subscribed and has to turn down many able candidates.
A statement from Bristol said: "The 'boycott' announced today by the Independent Schools Council is disappointing and based on a fallacy.
" The university does not practise
unfair discrimination, it does not operate quotas and it will continue to
recruit exceptionally able students from all backgrounds through a
selection process that is as fair and straightforward as we can make it.
"Pupils, not schools, make the decisions about which universities to apply
to and we are confident that they will continue to want to study at
The university's history department has been praised by the higher education minister Margaret Hodge for its policy of considering the school a candidate comes from in relation to his or her results.
So if students who apply from a school with generally poor results have relatively good grades or appear promising, they will be considered for a place.
The government is calling on universities to do more to encourage applications from pupils from less-advantaged backgrounds.
Under its plans to reform higher education funding, it will appoint an "access czar" to check universities are attempting to widen access before they are allowed to raise extra cash through top-up fees.
The government does not want to get embroiled in the row over Bristol.
A spokesman for the Department for Education and Skills said:
"This is a matter for the Independent Schools Council.
"Widening access is central to the government's ambition for higher education but individual admission arrangements are a matter for universities themselves.
"The government does not endorse any single admissions system. "