Top universities are becoming more exclusive, with fewer poor students admitted than a decade ago, Government advisers have warned.
In a new report, the Social Mobility and Child Poverty Commission also raises concerns that the proportion of state-educated pupils attending these institutions has dropped.
It suggests that the nation's most academically selective universities are becoming less socially representative, and have "a long way to go" to ensure that all potential students have a chance of gaining a place.
Alan Milburn, the Government's social mobility tsar, said that while it was clear that universities were increasingly determined to help make Britain socially mobile, it was time for leading institutions to "up their game".
The new report reveals that there were 126 fewer students from the most disadvantaged backgrounds at Russell Group universities in 2011/12 than there were in 2002/03. The Russell Group represents 24 of the UK's most selective universities, including Oxford and Cambridge.
The findings, based on an analysis of official data, show that the number of state school pupils starting a degree at a Russell Group university increased by 1,464 between 2002/03 and 2011/12.
But it adds that nearly half of the new places created at Russell Group institutions in the last decade have gone to private school students, with the number of privately-educated pupils increasing by 1,426. It means that overall the proportion of young, full-time state-educated undergraduates at Russell Group universities has fallen from 75.6% in 2002/03 to 74.6% in 2011/12.
And the proportion of state-educated young undergraduates from poorer families fell from 19.9% to 19% in the same period.
The report, which looks at the progress made in increasing access in the last six months, concludes that there are still around 3,700 "missing" state-educated students - those who have good enough grades to get into a Russell Group university, but do not get a place.
It also warns that many of the most academically selective universities - those asking for the highest A-level grades - are not setting high enough targets to close the "fair access gap".