State school pupils have won more places to study at Cambridge than in any year since records began, taking more than two thirds of spots at the university’s prestigious colleges for the first time, administrators have said.

More people from the UK’s most deprived areas will also be attending the elite institution next month, the admissions department added, increasing in number from just over 12% to 14% of the freshers cohort, further reducing the places awarded to private fee-paying schools.

It means the 2019-20 student body will have 68% from state schools in a progression that Cambridge described as “deeply encouraging”. But it remains unrepresentative of entrants to UK university courses more widely. For the last five years, close to 90% of students enrolling in higher education have come from state schools.

“We have been exploring different ways to identify talented students who will thrive on our courses and help to make our student population truly representative of the UK population,” said Dr Sam Lucy, director of admissions for the 29 Cambridge undergraduate colleges. “This has included challenging false perceptions that put off applicants. It is deeply encouraging to see that our actions to provide educational opportunity for all those who have the potential to study here are paying off.”

Private schools have pointed out that some of their applicants are on scholarships and bursaries, so are not necessarily from socially or economically advantaged backgrounds, but nevertheless Cambridge, along with other leading institutions such as Oxford University, have faced increasing pressure to diversify their student populations. Cambridge has pledged to admit a third of its intake from the most underrepresented and disadvantaged groups by 2035 and wants UK state-educated pupils to make up 69.1% of its intake by 2024-25.

“There is still a long way to go in improving representation given that about 93% of pupils are taught in state schools in England compared to the 68% admitted this year by Cambridge,” said Geoff Barton, general secretary of the Association of School and College Leaders. “State school pupils are also underrepresented at some other high-tariff universities. These institutions are increasingly recognising that exam grades are a blunt instrument and can serve to entrench educational disadvantage unless they are understood in their context. They are heading in the right direction in trying to address this situation and we appreciate that it is a complex process but it is frustratingly slow.”

Mike Buchanan, executive director at the Headmasters’ and Headmistresses’ Conference, which represents private school leaders, said it “supports broadening access to such universities for bright students from all backgrounds, provided measures of disadvantage are sophisticated and intelligently applied”.