The Sutton Trust charity said its school-by-school data on university entry showed "stark" differences.
BBC analysis of the data shows private schools often get more pupils into selective universities than state schools with similar results do.
Universities called for more freedom in offering places to bright state pupils.
The Sutton Trust has, for the first time, combined individual schools' A-level results with data from the university admissions body Ucas.
Its table shows, by individual school, what percentage of pupils went forward into higher education in general, and what percentage went to a list of 30 universities the charity considers "highly selective".
Continue reading the main storyA bright student is a bright student is a bright student... it doesn't matter what their school or educational background is, the interview will allow us to pull that out”End Quote Mike Nicholson Director of undergraduate admissions, Oxford University Four independent schools - Eton, Westminster, St Paul's Boys and St Paul's Girls - and state-funded Hills Road Sixth Form College in Cambridge, together sent 946 pupils to Oxford and Cambridge between 2007 and 2009.
By contrast, 2,000 lower-performing schools combined sent a total of 927 students to the two elite universities, getting less than 6% of available places, the Sutton Trust found.
Many of these schools sent no pupils at all, or on average fewer than one per year.
The BBC used the data to compare schools with similar average A-level points against each other, and found that the figures suggested a gap remained between independent and state schools' university admissions.
For example, among schools where pupils achieved an average of 801-850 A-level points each (900 is equivalent to three A grades), 26% of the comprehensive school pupils went on to the selective universities, compared with 45% of the independent school pupils.
Continue reading the main story And for schools with 851-900 A-level points per student, 50% of independent school pupils got places at the selective universities, while only 32% of comprehensive pupils did.Sutton Trust chairman Sir Peter Lampl said "stark inequalities" in university entrance were driven primarily by the exam results.
Independent and selective state schools tend to dominate the highest A-level grade scores.
But he added that the data "reveals that university chances can vary dramatically for schools with similar average grades".
The Trust also noted that pupils from high-attaining independent schools put in more applications to highly selective universities than comprehensive school peers with similar grades.
'Subjects are key'However, the Russell Group, which represents 20 leading universities, said it was concerned that the Sutton Trust report failed to explain fully the reasons behind the gap.
Universities say A-level subject choice is often a factor in place offersIt said a simple A-level point score did not show what subjects were taken, nor exactly what grades were achieved.
Professor Anna Vignoles of the Institute of Education has researched the issue.
She also notes that students with good grades may still not have studied the required subjects for certain courses.
And she adds that a points average might camouflage wide grade variation within an individual school.
But even so, there is still some disparity in acceptances between independent and state schools with similar grades which could not be explained away, she said.
"In our research, not all of that gap disappears even when you account for subject and choice at A-level."
Mike Nicholson, director of undergraduate admissions at Oxford, said that the university targeted state schools which had little or no history of sending pupils there.
In recent years, state school applications had risen, he added.
During the selection process, the university now flags up candidates with excellent results who are from disadvantaged backgrounds - whether from an under-achieving school, a postcode indicating deprivation, or time spent in the care system.
Such candidates may be fast-tracked to interview.
"A bright student is a bright student is a bright student... it doesn't matter what their school or educational background is, the interview will allow us to pull that out," said Mr Nicholson.
'Damning indictment'Universities UK, the vice-chancellors' umbrella body, called on the government to demonstrate a "strong will and commitment" in backing the use of such information - sometimes called "contextual data" - about deprived students' backgrounds, in university admissions processes.
In its recent White Paper, the government outlined plans to allow universities to offer as many places as they want to students with AAB grades at A-level.
These must "explicitly allow universities to use contextual data in the admissions process", said UUK president Professor Sir Steve Smith.
"However, we must make sure that efforts to increase the participation rate of disadvantaged students isn't focused solely on a handful of the most competitive courses and universities," he added.
The University and College Union said the report showed that an expansion of places for students with AAB grades "would most likely be filled by students from the most privileged backgrounds".
The National Union of Students called for changes to the admissions system, to allow university place offers to be based on actual rather than predicted grades, arguing that poorer students were more likely to receive inaccurate grade predictions.
Its president, Liam Burns, also called for more powers for the Office of Fair Access to tackle the "entrenched bias of some universities".
But the Schools Minister Nick Gibb said the report was a "damning indictment" of "Labour's failure to improve social mobility".
"Despite all their promises, they left hundreds of thousands of children with little to no chance of getting to the best universities," he said.
Mr Gibb said the government was tackling the problem by improving schools and targeting funding at the poorest pupils.
The Department for Education said it was planning to publish, from next year, school-by-school data on the proportion of pupils going on to university, as well as destinations of post-16 school leavers.
But critics, including Labour, argue that the government's decision to allow universities to charge up to ?9,000 per year in tuition fees is likely to put off students from deprived backgrounds.
The fees are paid up front by the government in the form of a loan, which is then paid back after the student graduates and is earning above ?21,000 a year.
The Office of Fair Access is due next week to publish the "access agreements" under which universities wanting to charge higher fees commit to targets for recruiting disadvantaged students.
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