Oxford University has been accused of "institutional bias" against black and minority ethnic students after figures revealed that white applicants to some of the most competitive courses are up to twice as likely to get a place as others, even when they get the same A-level grades.

Figures for applications to the university in 2010 and 2011, obtained by the Guardian under the Freedom of Information Act, revealed that 25.7% of white applicants received an offer to attend the university, compared with 17.2% of students from ethnic minorities.

White applicants to medicine, one of the most prestigious courses, were twice as likely to get a place as minority ethnic candidates, even when they had the same triple A* grade A-level scores.

Older figures for Cambridge university suggested a similar pattern.

David Lammy, the Labour MP for Tottenham, who has been a vocal critic of the university application system, said the figures suggested "institutional bias" and proved institutional failure.

Both Oxford and Cambridge, the country's most prestigious universities, have faced questions over the varying success rates of applicants from different ethnic groups. The gap has often been explained as being due in large part to the fact that students from ethnic minorities are more likely to apply for the most competitive courses, such as medicine.

But the latest figures, which for the first time break down success rates by both ethnicity and grades for some of Oxford's most competitive subjects, cast significant doubt on these long-running explanations.

They show that white students were more than twice as likely to receive an offer to study medicine as those from ethnic minorities. The disparity persisted for the most able students: 43% of white students who went on to receive three or more A* grades at A-level got offers, compared with 22.1% of minority students.

For economics and management, the university's most competitive course, 19.1% of white applicants received offers, compared with 9.3% for ethnic minorities. Among the most able, these success rates rose to 44.4% and 29.5% respectively.

There was, however, no statistically significant difference in success rates between white and non-white students when applying to study law at the university.

The issue of race at Oxbridge has regularly hit the headlines, particularly since 2010, when data obtained by Lammy showed, among other disparities, that just one British black Caribbean undergraduate was admitted to Oxford in 2009, a figure later cited by David Cameron.

"When I first raised these issues in 2010, Oxford explained that the figures were due to the prevalence of black and minority ethnic [BME] candidates applying to the most competitive courses," Lammy said. "This new evidence blows that apart. We now know BME students get fewer offers even with the same grades. Where there are interviews and quite large hurdles at the application stage, as with Oxbridge, it is for the universities to demonstrate there is not institutional bias. These figures suggest institutional bias, and certainly show sustained institutional failure."

He acknowledged that in the last couple of years the two universities had made renewed efforts to recruit BME candidates. "That should be welcomed, but what we need is a step change, and that hasn't happened yet."

Admissions tutors don't necessarily know the ethnicity of candidates who don't make it to the interview process, although they do see their full name and details of their schooling, a spokeswoman confirmed. Admissions statistics do show that students from ethnic minorities apply disproportionately to competitive subjects, but that doesn't account for the discrepancies within subjects demonstrated by the figures.

The University of Cambridge refused an FoI request for the same detailed breakdowns by subject and grade, saying it was too costly to be handled under the act. However, it did provide some older figures dating from 2007-09, before the A* grade was introduced for A-levels, which show similar patterns to Oxford.

These figures show the ratio of offers to study medicine at the university to applicants who achieved at least three A grades at A-level was 35% for white students compared with 24% for minority ethnic students, while for law the figures were 38% and 32% respectively.

Both universities rejected any suggestion that discrepancies in application success rates for different ethnic groups were a result of discrimination.

Oxford said it was closely examining the phenomenon. "Oxford University is committed to selecting the very best students, regardless of race, ethnicity, or any other factor," a spokeswoman said. "This is not only the right thing to do but it is in our own interests. Differences in success rates between ethnic groups are therefore something we are continuing to examine carefully for possible explanations. We do know that a tendency by students from certain ethnic groups to apply disproportionately for the most competitive subjects reduces the success rate of those ethnic groups overall. However, we have never claimed this was the only factor in success rate disparities between students with similar exam grades.

"We do not know students' A-level grades when selecting, as they have not yet taken their exams. Aptitude tests, GCSEs and interviews, which are used in our selection process, have not been explored in this analysis and are important in reaching reliable conclusions."

A spokeswoman for Cambridge said the analysis of the FoI figures was superficial and "ignored a significant number of relevant variables", such as subject mix, and performance in entry tests and interviews. "Admissions decisions are based on students' ability, commitment and potential to achieve," she said. "Our commitment to improving access to the university is longstanding and unwavering … We aim to ensure that anyone with the ability, passion and commitment to apply to Cambridge receives all the support necessary for them to best demonstrate their potential."

Rachel Wenstone, vice-president of higher education at the National Union of Students said: "My initial response to these figures was shock – this is quite frightening. Quite clearly, there appears to be some structural discrimination in some departments at Oxford, and the university needs to deal with it immediately.

• See the full data and methodology on the datablog.

• If you are from an ethnic minority background and applied to Oxford or Cambridge, we'd be interested to hear about your experiences. Whether good or bad, successful or not, let us know in the form below, along with how we can get in touch with you.