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".
The report claims that even if every Russell Group university was to meet the targets they have set for themselves for 2016/17 on increasing the numbers of state school students then it would only cut the numbers of "missing" pupils by a quarter.
The Commission says it is "deeply concerned" about the lack of progress being made on ensuring pupils have a fair chance of a university place.
"The most selective universities need to be doing far more to ensure that they are recruiting from the widest possible pool of talent.
"The Commission will be looking for evidence of a step change in both intention and action in the years to come."
Mr Milburn, chair of the Commission, said: "It is clear that there is an increasing determination on the part of our universities to do their bit in creating a Britain that is more socially mobile.
"But we cannot be complacent: there is a long way to go to ensure that there is fair access to our best universities. They need to up their game."
Dr Wendy Piatt, director general of the Russell Group, said she was pleased that the Commission had acknowledged that the higher education sector takes the issues of social mobility and fair access seriously.
But she warned that the many reasons why state-educated pupils and poorer students are under-represented cannot be solved by universities alone.
"Ultimately too few students from some state schools get the right grades in the right subjects and even those who do are less likely to apply to leading universities.
"Whilst we accept the Commission's figures for the specific dates they have chosen to highlight, it's worth noting that there will be some fluctuation in these numbers year on year and this has an impact on the figures.
"Looking back at the period from 1997/98 to 2010/11, there was an increase in the proportion of students from state schools enrolling at Russell Group institutions from 69.5% in 1997/98 to 74.7% in 2010/11".
The report comes just weeks after the Office for Fair Access (OFFA) warned that England's top universities have made "little or no headline progress" in recruiting students from poorer families in recent years.
Despite making a considerable effort and spending millions of pounds, the performance of these selective institutions has remained flat, it said.
OFFA director Professor Les Ebdon said that an "unacceptably large'' gap remains between the numbers of rich and poor students attending leading universities.
The Commission makes a number of recommendations, including calling for clear targets to be set to improve access and for universities to make more use of "contextual data" - information about a student's background - when making offers.
Universities Minister David Willetts said: "We are committed to improving social mobility, and are pleased that this year the level of university applications from the most disadvantaged 18-year-olds are at their highest proportion ever."