Oxford has rejected plans drawn up by David Cameron to force top universities to disclose the proportion of ethnic minority applicants given places, saying it “does not see the need” for such legislation.

The Prime Minister specifically mentioned the university in a call for widespread reforms, writing in the Sunday Times that black people were “more likely to be in a prison cell than studying at a top university”.

Mr Cameron said it was “striking” that only 27 black students started at Oxford University in 2014, of an intake of more than 2,500 people.

But the university defended its record, saying 367 undergraduates from ethnic minority backgrounds received places in 2015, up 15 per cent in five years.

A spokesman for Oxford said the university welcomed “discussions” about the information it publishes, but rejected the need for a change to the rules.

And he said the university was doing well against “a challenging backdrop of changes to the educational landscape”.

“The effects of social inequality are already pronounced before children begin formal schooling, and universities, schools and government must work together to address their root causes effectively,” he said.

The director general of the elite Russell Group of universities, Wendy Piatt, also defended the “good progress” member institutions have made – and suggested poor teaching at school level was to blame.

She said: “There are still far too many children from disadvantaged backgrounds underachieving at school and receiving poor advice and guidance. It will take time, commitment, and sustained action from a range of agencies to raise pupils' aspirations, increase attainment and improve the advice and guidance offered.”

Sir Anthony Seldon, the vice-chancellor of the University of Buckingham and one of Mr Cameron’s biographers, welcomed the Prime Minister’s push.