Just 100 schools and colleges account for a third of all admissions to the country's top two universities. Over 80 per cent of the schools are in the independent sector, which educates just 7 per cent of pupils, research by the Sutton Trust shows.
Sir Peter Lampl, the chairman of the trust, said the figures were "deeply worrying" for bright pupils at state schools.
"It is a sad waste of talent that the chances of reaching one of these highly selective universities are significantly greater for those who attend a small number of the country's elite fee-paying schools," he said. "Where does this leave the vast majority of the population who do not have access to these opportunities?"
The study followed the university destinations of pupils at 3,700 schools between 2002 and 2006 by analysing the Ucas admissions database.
The top 100 schools account for less than 3 per cent of schools and colleges offering post-16 qualifications.
Yet they provided more than one-sixth of all students to the country's leading 13 universities identified by researchers. These are Birmingham, Bristol, Cambridge, Durham, Edinburgh, Imperial, LSE, Nottingham, Oxford, St Andrews, UCL, Warwick and York.
Pupils at top performing state schools are significantly less likely to win places at leading universities, even when they achieve good results, the report said.
The proportion of university entrants going to Oxbridge from the top 30 independent schools was nearly twice that of the top 30 grammars, despite similar A-level results, according to the research.
At the top 30 comprehensive schools, only half the expected number of pupils won places at the country's best 13 universities when the relationship between average A-level results and university admissions was taken into account.
The report follows criticisms made last week by John Denham, the new secretary of state for innovation, universities and skills, that elite universities are guilty of class bias against pupils from state schools.
The latest figures from the Higher Education Statistics Agency show that at Cambridge, 57.9 per cent of students are from state schools. At Oxford, that figure is 53.7 per cent, significantly below a benchmark of taking 75.4 per cent of its students from state schools.
A spokeswoman for Oxford University said that it aimed to recruit the most able students regardless of background.
"While it is the case that a small number of schools do send a large number of pupils to our university, the reverse is also true: a large number of schools send a small number of pupils.
"This shows that we are successfully reaching people in schools where the straight-A student is in a minority," she said.
The Sutton Trust, an education charity which aims to improve social mobility, has committed at least pound;10 million over the next five years to widen access to leading universities.
It is calling on independent schools and leading state schools to be opened up to more children from poorer backgrounds.
HOW THE SECTORS COMPARE IN THE RACE FOR TOP UNIVERSITY PLACES
Top ten independent schools
Westminster School 85.6 (703)
St Paul's Girls' School, London 85.2 (391)
Winchester College 82.8 (529)
St Paul's School, London 80.4 (632)
North London Collegiate School 76.9 (444)
Wycombe Abbey School 76.9 (269)
Eton College, Windsor 75.7 (921)
Haberdashers' Aske's School for Boys, Herts 71.5 (562)
Haberdashers' Aske's School for Girls, Herts 71.1 (398)
King's College School, Wimbledon 70.8 (516)
Top ten selective state schools
Royal Grammar School, High Wycombe 81.9 (388)
Queen Elizabeth's School, Barnet 61.8 (375)
Henrietta Barnett School, London 54.7 (298)
Colchester Royal Grammar School 54.5 (293)
King Edward VI Camp Hill Boys, Birmingham 52.5 (241)
St Olave's Grammar School, Orpington 52.5 (349)
Reading School 52.1 (309)
Tiffin Girls School, Kingston, Surrey 51.4 (310)
Latymer School, Edmonton, north London 47.9 (519)
Pate's Grammar School, Cheltenham 46.2 (374)
Top ten non-selective state schools
London Oratory School 62.4 (186)
Watford Grammar School for Boys 46.3 (348)
Beeslack Community High School, Scotland 41.3 (112)
Lady Margaret School, London 40.8 (102)
Watford Grammar School for Girls 39.9 (307)
JFS School, Harrow, Brent 38.1 (296)
Dame Alice Owen's School, Potters Bar, Herts 36.6 (310)
Hills Road Sixth Form College, Cambridge* 36.2 (1249)
Cardinal Vaughan School, London 32.6 (190)
King Edward VI College, Stourbridge* 30.9 (845)