Oxford and Cambridge are being accused of being so socially exclusive that they recruit more students from eight top schools than almost 3,000 other English state schools put together.
The Sutton Trust social mobility charity says the leading universities are failing to attract a wide enough range of talent.
Trust founder Sir Peter Lampl said all young people needed a "fair chance".
Oxford University said they were "very aware" that they "must work harder".
The study examined Oxford and Cambridge admissions data between 2015 and 2017 and found a handful of schools, mostly private, disproportionately dominating the number of places awarded.
The Sutton Trust says pupils from eight schools filled 1,310 Oxbridge places over three years, compared with 1,220 from 2,900 other schools. These 2,900 schools were those with historically few admissions to Oxbridge - and accounted for about three-quarters of secondary schools. In the past three years, Oxford and Cambridge admitted a total of 19,851 undergraduates, with the remainder of places coming from other private schools and top performing state schools and colleges.
The research also found that high-achieving independent school pupils were twice as likely as state school pupils to apply to Oxford and Cambridge, even with the same ability and predicted grades.
The report shows the imbalance in admissions:
l 7% of all UK pupils attend private schools
l 18% of those taking A-levels are at private school
l 34% of Oxbridge applications are from private school
l 42% of Oxbridge places go to private school pupils
The study says there are some parts of the country where particularly few young state-educated people get places.
The study blames a lack of advice and guidance for applicants and calls for better information about what is required for entry and for admissions to take into account young people's backgrounds.
Oxford runs summer schools to encourage more disadvantaged students to apply - and the university says there are plans to attract more students from places where it had recruited few students in the past.