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.