The vice chancellor of Cambridge University has told private schools they will have to accept that their pupils will be getting fewer offers of Oxbridge places in the future.
Prof Stephen Toope said although students from private schools would not be told "we don't want you" they will be "welcoming others" from different backgrounds.
Speaking to The Times, he said: "I would say we have to keep making it very, very clear we are intending to reduce over time the number of people who are coming from independent school backgrounds into places like Oxford or Cambridge."
"Individual students who are talented, we would want them, but they're going to be competing against an ever-larger pool because there are more students coming from state schools who are seeing a potential place for themselves at Cambridge or Oxford or other Russell Group universities."
Universities minister Michelle Donelan backed Prof Toope's view.
"It's really important that young people with the desire and ability go into higher education, including the very best universities, but that’s only part of the hurdle. It’s about making sure they complete those courses," she said.
But Conservative MP Robert Halfon, chair of the Commons Education Select Committee and the member for Harlow, said Cambridge and Oxford were still not doing enough to encourage applications from different backgrounds and cultures.
"There is clearly not a level playing field and very little has been done.
"We need to make sure there is a meritocracy, as at the moment it's not," he said.
Barnaby Lenon, chairman of the Independent Schools Council, said the issue was a complex one.
“Taxpayers expect that Oxford and Cambridge would select students based on their academic potential. How they do that is up to them. A proportion of the best students in the UK go to independent schools, very often on large bursaries," he said.
“A large proportion of those state school pupils at Oxford and Cambridge come from grammar schools or state schools in prosperous areas where there is selection by house price. Many come from wealthy homes overseas, but the overseas figures are rarely mentioned.
“Independent schools continue to get their best pupils into Oxford and Cambridge in large numbers because these are pupils with great academic potential. Their degree results at Oxford and Cambridge bear this out.”