More than one in four students starting at the University of Warwick in 2017 were privately-educated, according to the Higher Education Statistics Agency.
School of origin was recorded for 2,945 students aged under 21, who were starting a full-time, first degree at Warwick in the academic year 2017-18.
Of those, 705 came from independent, fee-paying schools - 24% of the cohort.
Across England, around 91% of secondary school students are state-educated - considerably higher than at Warwick, where 76 per cent of freshers came from state schools.
Social mobility charity the Sutton Trust said it expected to see more state school students getting into university. Founder Sir Peter Lampl said: "Getting a degree is the surest way to a good job, so improving access to higher education is central to social mobility."
The Sutton Trust has called for a reform of the admissions process, including making the personal statement simpler and allowing students to apply after they have received their A-level grades.
Sir Peter said: "The personal statement can act as an additional barrier to disadvantaged young people who are less likely to be supported in preparing it. Around 1,000 disadvantaged students per year have their grades under-predicted. We need universities to be more transparent as to what grades these students require."
The Higher Education Funding Council sponsors outreach programmes in deprived areas where young people are unlikely to go to university. Around 20 per cent of the young adult population come from these areas, but at Warwick, just 6 per cent of first years were in this category.
The Association of School and College Leaders said universities and the government need to do more to widen access to higher education.
General secretary Geoff Barton said: "The proportion of state school pupils at some universities is significantly out of kilter with the fact that the vast majority of people attend these schools, including many young people from disadvantaged backgrounds."
He said students from low-income families may be unable to afford the cost of living away from home, reducing their university options, adding: "The level of funding in the state education system is totally inadequate, making it difficult for schools and colleges to provide the extra-curriculars which benefit independent school pupils and strengthens their applications."