England's most selective universities are still taking a lower proportion of state school teenagers than many other institutions, figures suggest.
New data shows that the percentage of state-educated youngsters studying for a degree varies widely between universities.
At some institutions virtually all students went to a state school, while at others the proportion is less than two thirds.
In addition, just over one in 10 (11.3%) of entrants in 2015/16 were from "low participation" neighbourhoods - those areas that do not send many students on to higher education. This is down from 11.4% last year.
The figures come amid a continued push by government and higher education to widen participation, encouraging students from all backgrounds to study for a degree.
Overall, 89.9% of UK young, full-time undergraduates starting courses at British universities in 2015/16 were educated in the state sector, according to figures published by the Higher Education Statistics Agency (HESA), a similar proportion to the year before (89.8%).
In England alone, 89.8% of entrants were state educated.
A breakdown of the figures shows differences between universities, with all Russell Group universities - those that typically ask potential students for high-entry grades and are often considered the best in the country - are in the second half of the table.
Oxford, which has the lowest proportion of state educated students, excluding small specialist colleges, has seen a drop in entrants from this background, with 55.7% of its intake in 2015/16 from state schools and colleges, compared to 57.7% five years ago in 2011/12.
All other Russell Group institutions have seen an increase in the percentage of state educated students in the last five years.
Among English universities, again excluding smaller specialist colleges, Liverpool Hope University had the highest percentage of state school pupils at 99.4%, followed by Bolton at 99.3% and Bedfordshire at 99%.
At the other end of the scale, besides Oxford, 60.5% of Durham's entrants were state-educated, along with 61.4% of those starting at Bristol, 61.9% of entrants to Cambridge and 65.5% of entrants to Imperial College, HESA's figures show.
The Russell Group university with the highest percentage of state school pupils starting in 2015/16, was Liverpool at 88.8%, followed by Queen Mary, University of London at 88.7%.
Among these top universities outside of England, 85.9% of Cardiff's 2015/16 entrants were from state schools and colleges, along with 69.7% of those starting at Edinburgh, 84.6% of those going to Glasgow and 98.4% of those at Queen's University Belfast.
Universities Minister Jo Johnson said: "With record high proportion of young people from state schools entering university, these statistics show that more students are being given the opportunity to reach their full potential, regardless of their background.
"But they also show that there is more to do at some universities, where there are still too few students progressing from the most disadvantaged backgrounds.
"That is why our reforms to higher education, including the introduction of the Office for Students and the Teaching Excellence Framework, are putting access and support for students at the heart of the system."
Dr Samina Khan, director of undergraduate admissions and outreach at Oxford University, said: "We are constantly working to increase our intake of students with academic potential from under-represented backgrounds through a range of widening participation activities.
"Figures released last month by Ucas show that our offer rates for students from low-participation areas are outperforming the rates that would be expected given predicted grades and subject choice.
"We are also expecting to increase our proportion of state school students for 2016 entry, having made more than 59% of offers to state-educated applicants in this cycle.
"However, we are aware that there is still progress to be made, and we will continue to work hard to encourage more successful applications from under-represented groups."
HESA's figures on students from "low participation neighbourhoods" show that Sunderland University has the highest proportion of entrants from this group at 29.7%.
At the other end of the scale, 3% of University College London's entrants in 2015/16 were from these neighbourhoods, along with 3.1% of those at Cambridge. This excludes specialist colleges.
The latest figures cover UK full-time first degree students.