A spokesperson for Cambridge said that its admissions decisions were made on academic considerations alone, while spending £5m a year on access measures including work with black and minority ethnic school pupils.

“The greatest barrier to participation at selective universities for students from disadvantaged backgrounds is low attainment at school. We assess the achievements of these students in their full context to ensure that students with great academic potential are identified,” the spokesperson said.

“Widening participation further will require government, schools, universities, charities, parents and students to work closely together. We will continue to work hard with all parties to raise aspirations and attainment to improve access to higher education.”

The data emerged after a long-running tussle between Lammy and Oxford, with Oxford refusing to publish detailed breakdowns of its admissions decisions by ethnic group despite repeated requests, including a direct approach by Lammy to Oxford’s vice-chancellor.

Lammy’s initial request for the ethnicity data last year was refused by Oxford, despite Cambridge supplying the breakdown of offers and applications and Oxford itself having produced the same data in 2010.

The former education minister – who has campaigned for years over widening access to top universities – remained unhappy that Oxford refused to release detailed figures showing offers to British students of Caribbean and African descent. that only one black Briton of Caribbean descent had been accepted as an undergraduate at Oxford in 2009.