State schools provided more than 95% of students starting at Anglia Ruskin University in 2017, according to the Higher Education Statistics Agency.
School of origin was recorded for 2,210 students aged under 21, who were starting a full-time, first degree at Anglia Ruskin - which has a Peterborough campus -in the academic year 2017-18.
Of those, 2,125 were state-educated - 96% of the cohort.
Across England, around 91% of secondary school students are in state schools, and 90% of first-year university students.
At 10 British institutions, less than two-thirds of new starters were state-educated.
Social mobility charity the Sutton Trust said getting a degree is “the surest way to a good job”.
Founder Sir Peter Lampl said: “Improving access to higher education is central to social mobility.”
“All young people should have an equal chance of getting into university, particularly the most selective ones.”
The Sutton Trust also said that the admissions process, especially the personal statement, can act as a barrier to disadvantaged young people.
Sir Peter added: “We have made the case for giving poorer students a break on the grades they need for admission.”
The Higher Education Funding Council sponsors outreach programmes in deprived areas where young people are unlikely to go to university.
Around 20% of the young adult population come from these areas, and at Anglia Ruskin, 16% of first years were in this category.
The Office for Students says there is a “huge spread” of advantaged and disadvantaged students within the state sector.
Chris Millward, director for Fair Access and Participation, said: “Schools in deprived areas are less likely to send students to higher education.
“We work with universities to improve access for young people from disadvantaged backgrounds, from outreach programmes in schools to supporting them through their degree.”
The OfS said every university charging above £6,000 a year in tuition fees must have a plan to improve equality of access to higher education.