The proportion of poorer students at some of the UK's leading universities has fallen in the past decade despite attempts to boost numbers.
Press Association analysis of official data shows the overall proportion of more disadvantaged students starting at a Russell Group university - considered the best in the country - has stalled in the past 10 years.
The findings come weeks after Prime Minister David Cameron warned educational institutions they need to do more to tackle social inequality.
Around one in six (17.2%) students from lower social groups started a course at a Russell Group institution last year, compared with nearly one in three (32.1%) of their wealthier peers.
One charity leader said it was "worrying" that the gap has widened at some universities.
The Russell Group said progress is being made to ensure able students from all backgrounds have access to its universities, but it cannot solve the problem alone.
Out of the 24 Russell Group universities, Oxford had the lowest proportion of entrants from lower social backgrounds at one in 10, the analysis shows, followed by Cambridge with 10.2%.
Ten years ago, poorer students made up around one in eight Oxbridge entrants.
Queen Mary University of London had the highest proportion with more than a third of entrants (37%) from disadvantaged backgrounds, followed by Queen's University Belfast at 31.9%.
Almost a third of Russell Group universities - seven institutions across the UK - have seen a drop in the proportion of poorer entrants in the past decade, the analysis shows.
Exeter has seen the biggest fall, down 2.6 percentage points compared with 2004/05. Others include Oxford (down 2.3), Cambridge (down 2.2), Durham (down 1.4), Imperial College London (down 2.5), Glasgow (down 1.3) and Queen's University, Belfast (down 2.5).
King's College London has seen the biggest rise in poorer students - up 5.7 percentage points.
On average, students from poorer backgrounds made up around one in five entrants (20.8%) to Russell Group universities in 2014/15, compared with 19.5% a decade ago.
In comparison, disadvantaged students make up more than a third (37.5%) of entrants to other UK universities.
The results are based on data on social classes published by the Higher Education Statistics Agency (HESA) for the past 10 years. HESA has announced it is discontinuing the social classes measure.
The falls come despite attempts by universities and successive governments to widen access to higher education - particularly the most selective institutions.
As part of major reforms that saw tuition fees in England rise to £9,000, English universities wishing to charge this amount have to sign access agreements with the Office for Fair Access (OFFA). These documents, tailored to each institution, set out legally binding targets on areas such as disadvantaged students.
Wendy Piatt, director-general of the Russell Group, said: "Ensuring our doors are wide open to talented and able students from all backgrounds really matters to us and real progress is being made. Last year 1,760 more students from low socio-economic backgrounds went to a Russell Group university than in 2009.
"The number of students eligible for free school meals going to our universities has doubled in the last four years, and the number of black and minority ethnic students has increased by more than a third since 2012."
Universities spend hundreds of millions of pounds each year on bursaries, scholarships and work with schools and colleges, she said.
"While our universities invest a huge amount of time, effort and resources into improving the situation, they cannot solve this problem alone," Dr Piatt added.
"There are still far too many children from disadvantaged backgrounds underachieving at school and receiving poor advice and guidance. It will take time, commitment and sustained action from a range of agencies to raise pupils' aspirations, increase attainment and improve the advice and guidance offered."
Lee Elliot Major, chief executive of social mobility charity the Sutton Trust, said: "It is good to see that the proportion of state school students entering top universities has risen over the past decade. However it is worrying that the access gap between those from poorer backgrounds and their more advantaged peers has actually widened at some universities.
"Today's figures tell us that we need renewed and concerted efforts from Government, schools and universities alike to improve participation rates for the poorest students."
Oxford said it has legally binding targets with OFFA which it is working towards and focus on categories of disadvantage rather than school type or self-reported socio-economic class.
A University of Exeter spokesman said: "We are deeply committed to widening participation and engaging and inspiring disadvantaged students, whether that means progression to the University of Exeter or higher education more generally. We are actively committed to further increasing the diversity of our student population."
Universities Minister Jo Johnson said: "These figures underscore a worrying lack of progress at some institutions and underline how vital it is that highly selective universities redouble their efforts to reach out to students from disadvantaged backgrounds. There is still much more to do to boost social mobility, which is why we plan to legislate for a new transparency duty to shine a spotlight on university admissions processes."
A Glasgow University spokesman said: "The University of Glasgow runs extensive and extremely successful outreach programmes to ensure that we recruit the most able and ambitious students regardless of socio-economic background. This is seen in the rise in the number of Scottish based students from the 40% most disadvantaged areas to more than 25% of our undergraduate intake – easily the highest of any of Scotland's Ancient Universities. We work closely with the Scottish Government as part of our Outcome Agreement to ensure that widening participation is core to our recruitment strategy."