Pupils from state schools and ethnic minorities are less likely to obtain an offer from one of the country's top universities than their white, privately educated peers even when they achieve the same A-level grades, a study has found.

Research by Durham University that will be published in the British Journal of Sociology in June found that state school pupils needed up to one grade higher than their peers at fee-paying schools to stand the same chance of receiving an offer from members of the Russell Group, the 24 most prestigious universities in the UK.

Dr Vikki Boliver, the author of the study, found that black, Pakistani and Bangladeshi pupils also required up to one grade higher at A-level than their white counterparts to stand the same chance of receiving an offer.

The study looked at 49,000 university applications between 1996 and 2006. The research found state school pupils were as likely to apply to Russell Group universities as their privately educated peers only if they had two higher A-level grades.

"Access … is far from 'fair'," Boliver said. "We need not only to continue the widening participation work already being undertaken but also to take a closer look at the admissions process."

The Russell Group said students from ethnic minorities were more likely to apply for the most competitive courses, such as medicine and economics, which required the highest grades. It said many good students at state schools had not studied the subjects required for its courses.

Criticising some students' "poor choices", Dr Wendy Piatt, director general of the Russell Group, said: "Universities need students not only to have good grades, but grades in the right subjects."