Record numbers of state-school pupils are going to top universities, figures showed this week.
Between 19978 and 20023 the number of students from state grammars and comprehensives admitted to the 13 leading universities increased by almost 6,000, or 35 per cent - suggesting that pressure from the Government to widen access is working.
But ministers said they will review university admissions targets because they are unfair on some institutions.
Universities are unhappy about the latest targets which they fear could lead to them having to "dumb down".
State-educated pupils now make up 68 per cent of new undergraduates at the top universities, compared with 61 per cent in 1997-8, according to the report from the Sutton Trust, an education charity that helps children from poor backgrounds.
It found that 22,979 students from state schools were admitted to universities such as Oxford, Cambridge, Birmingham, Bristol and Warwick in 20023, compared with 16,909 five years earlier.
This rise in numbers means a total of 15,000 extra state school pupils have studied at top universities over the five years period.
York (80 per cent), Birmingham (79 per cent) and Warwick (78 per cent) have the highest state-school intakes. Cambridge has 58 per cent, and Oxford has the lowest with 55 per cent - up from 52 per cent and 47 per cent respectively in 19978.
The report found that some of the targets were unjustifiable because of the way they are calculated, and could lead to universities having to "dumb down".
The row centres on targets for Oxford and Cambridge universities, which have risen sharply.
In September, targets for Cambridge rose from 68 per cent state-school entrants in 20012 to 77 per cent, while Oxford's went from 69 per cent to 77 per cent.
Fears were raised that universities would be forced to lower their standards to accommodate more state-school students, with Michael Beloff, president of Trinity college, Oxford, urging the Government to "take its tanks off Oxford's lawns".
The Sutton Trust said the new targets or benchmarks overstated the number of students with appropriate qualifications because they use total Ucas points rather than A-level grades. That means a student with a large number of low-grade vocational passes would score the same as one with a small number of high-grade A-level passes, even though only the A-level student could enter a top university.
Sir Peter Lampl, chairman of the Sutton Trust and a member of the Government's taskforce on university admissions, said: "Ministers should not allow the controversy over the new benchmarks to undermine the success of a range of outreach initiatives.
"On the one hand, we have a real success story; on the other, we face a continuing challenge.
"There are still 3,000 state-school students who each year achieve the A-levels necessary to enter our leading universities but who, for a variety of reasons, do not end up there."
Kim Howells, the higher education minister, said he would review the matter.
"It is a shame that this year's benchmarks caused such a storm," he said.
"Our universities are getting better at opening up their doors to a wider group of students. I am looking at the benchmarks to see if there is any way they can be improved and better understood by all people concerned."
The other universities included in the study were: Durham, Edinburgh, Imperial, the London School of Economics, Nottingham, St Andrews, University College London, and York.
The report, called State school admission to our leading universities, can be found on the Sutton Trust website at www.suttontrust.com