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Oxford and Cambridge universities have both increased the proportion of state school pupils they take - but are still falling short of targets.Official figures show that in 2008-9, 54.7% of Oxford's new undergraduates were from state schools. At Cambridge, 59.3% of new students were.
About 17% of sixth-formers in England are educated in the private sector.
All universities in the UK are set "targets" - known as benchmarks - on admitting state school pupils.
These are set by the bodies which fund universities.
For 2008-9, both Oxford and Cambridge had a target for just under 70% of new full-time undergraduates from state schools.
The way the targets are calculated changed for that year, leading to lower ones for both institutions - but both still say futher refinements are needed.
Both have shown an increase in the proportion of state school pupils admitted, data released by the Higher Education Statistics Agency (Hesa) show.
In 2007-8, Cambridge admitted 57% of its new undergraduates from state schools and Oxford 53.4%.
A spokeswoman for Cambridge University said: "The university welcomes the way in which this year's performance indicators reflect its efforts on widening participation, with state sector admissions reaching a high point of 59.3%, up more than 2 percentage points on the previous year's figure.
"The university makes great efforts to ensure that bright students from all backgrounds are admitted to Cambridge, and we are committed to maintaining those efforts in the future."
Encouraging ambition
A spokeswoman for the University of Oxford said: "Our latest admissions statistics are one year ahead of the Hesa figures. They relate to students who started in October 2009, showing the proportion of Oxford University's UK undergraduates who come from state schools at 53.9 %.
"These are more up to date than the Performance Indicator figures, which relate to entry 2008.
''There are many economic and social factors which can prevent students reaching their full academic potential by 18. For our part, we are doing our utmost to encourage academic ambition from a young age by working with students from 11 up, and by working closely with parents and teachers."
Hesa data released on Thursday also includes drop-out rates. Both Oxford and Cambridge score well on that, with more than 98% of their young entrants staying at the universities.
The average for the UK that year was just under 90%.
In Scotland, St Andrews University took 60.7% of its new entrants from state schools, against a target of nearly 74%.
Edinburgh University had 70.8% of its new intake from the state sector, against its target of 78.7%.
Both showed a slight improvement on the year before.
In Wales and Northern Ireland, all universities exceeded their targets.
Other universities in England highlighted by Hesa as being down against their targets on state school admissions included Bristol (60% against a target of 74.9%), Durham (59.2% against a target of 74.6%), Exeter (70.9% against a target of 78.7%) and Oxford Brookes University (71.6% against a target of 90%).This article is from the BBC News website. ? British Broadcasting Corporation, The BBC is not responsible for the content of external internet sites.