Oxford University is under fresh attack for failing to open up places to students from disadvantaged and ethnic minority backgrounds.

The latest annual admissions statistics report by the university showed just 11% of UK undergraduates came from disadvantaged areas, up from 7% in 2013.

The proportion of students identifying as black and minority ethnic was 18% last year, up from 14% in 2013.

There was a slight increase in the number of admissions from state schools during the same period, from 57% to 58%.

Labour MP David Lammy, who has repeatedly criticised Oxford and Cambridge over their records on admissions, said the figures showed little had changed in recent years.

“The progress is glacial. The truth is that Oxford is still a bastion of white, middle class, southern privilege. That is what it is,” he told the BBC Radio 4 Today programme.

“They have to explain why you are twice as likely to get in if you are white as if you are black and why you are more likely to get in if you are from the South than the North of England when you apply.

“Thirty black pupils applied for computing last year. Not one of them gets in. Are we really saying there isn’t a black student in Britain who can apply for computing who is worth a place at Oxford? Surely not.”

Universities Minister Sam Gyimah, who is black and went to Oxford, said the institution needed to “double down” on its work to engage with potential applicants at an earlier stage.

He said he did not seen any institutional bias, but added: “Where I think we need further and faster progress is that it’s not enough for the universities just to work with those who are applying at the A-level stage, they need to start earlier because the students that are successful actually start their preparation a lot earlier.

“It’s about raising aspirations, it’s about helping prepare students at the GCSE level and then when it gets to application stage, knowing how to actually play the system.”

Calling for Oxford to cast its net wider, he told BBC Radio 4’s World at One: “The challenge here is that unless the university doubles down to reach out and engage with lots more pupils across the country, they cannot honestly say that every potential applicant has a fair crack of the whip, and that is where the problem is.”

Samina Khan, the director of undergraduate admissions, acknowledged white British students were twice as likely to be admitted as black British students, but said the university was working hard to change.

“The reason for that is that you are looking a very different applicant pools. One is very large – that is the white pool in terms of who gets three As and above (at a A-level) – and the other one is very small,” she told the Today programme.

“We are not getting the right number of black people with the talent to apply to us and that is why we are pushing very hard on our outreach activity to make sure we make them feel welcome and they realise Oxford is for them.”

The measures included an expansion of its UNIQ spring and summer schools, which work with students from under-represented backgrounds.

“We are doubling the UNIQ summer school. We know it works. It is targeted at disadvantaged students and once they are on it and they apply to Oxford they are more likely to get a place from compared to the rest of the UK population,” Ms Khan said.

“Progress is much better than most people think. We will continue to work hard. I think the expansion of UNIQ, so that we are bringing 1,350 students to the university every year, will increase the pace of change.”