London: A Labour member of Parliament has accused Oxford and Cambridge universities of practising "social apartheid" because his just-published report on Oxbridge admissions reveals that many colleges are taking in very few black students while others are accepting none at all.

David Lammy, 45, who is black himself, acknowledged that some individual colleges and tutors are taking steps to improve access, but added that in reality, "many Oxbridge colleges are still fiefdoms of entrenched privilege, the last bastions of the old school tie".

His figures, which Lammy obtained by using the Freedom of Information Act, shows that British students of Pakistani origin also find it difficult to get into Oxbridge.

Out of every 100 Pakistani candidates who apply for a place, fewer than one gets an offer.

The corresponding figure for British Indian students is remarkably high - about one in three.

The hit rate in Bhikhu Parekh's family was 100 per cent - all his three sons, Raj, Nitin and Anant, got into Oxford and with scholarships.

Parekh, a prolific author and now a Labour peer aged 82, was for many years professor of political theory at Hull University and took time out of life in England to be vice-chancellor of Maharaja Sayajirao University in Vadodara between 1981 and 1984.

He is sympathetic towards Lammy's mission.

"Oxbridge need to do far more to recruit black and minority ethnic students," he told The Telegraph. "They can't obviously bend or break their rules of admissions but can still do much more within their limits."

Parekh added: "British Indians are doing much better than other communities because they have a long tradition of going to Oxbridge, are generally more wealthy, send their children to top schools and provide a stable environment. I don't like quotas but could go for positive action in favour of other communities."

One solution that Oxbridge or indeed higher education establishments in Britain have not tried nor is likely to is a reservation or quota system so that black and Pakistani students are allowed in with inferior marks so as to redress the balance.

Lammy found that between 2010 and 2015, only three of Oxford's 32 colleges made an offer to a black A-level applicant every year.

Figures for Cambridge University reveal that for each of the six years, on average, a quarter of colleges failed to make any offers to black British applicants.

According to Lammy, less than 1 per cent of offers went to Pakistani applicants, and in 2015, as many as 14 of Cambridge's 29 colleges did not make a single offer to a Pakistani applicant.

This year, the Pakistani student who did get in is Malala Yousafzai who is at Lady Margaret Hall, reading PPE (philosophy, politics and economics). Her precise A-level results are not known but she got the three A grades that were required.

Normally, the conditional offers are much tougher - either three A*s or two A*s plus an A. Those who miss the target, by however narrow a margin, suffer the heartache of being rejected.

The problem basically is that there are far too many candidates with three A*s chasing too few places.

Requested by The Telegraph, Cambridge University provided some typical statistics for British Indian students in 2016.

There were 508 applications, 171 offers (33.7 per cent) and 152 ( 29.9 per cent) acceptances. The overall success rate at Cambridge was slightly lower - 26.4 per cent.

As to why Indian children do so well, the answers involve social and cultural factors plus the very simple one that Indian parents are very driven and make sure their sons and daughters do their homework and revise for exams.

But for the health of society, the problem that Lammy has identified does need to be solved.

Currently, dons at individual colleges pick their students. But Lammy said moves such as a centralised admission process and the rollout of foundation year programmes for black pupils with potential could help address the balance.

A spokesperson for the University of Cambridge said its decisions on admissions were based on academic considerations alone.

"We are committed to admitting the best students who will thrive on our courses," he said, revealing it spends £5 million a year on access measures, which include work focused with black and ethnic minority students.

"The greatest barrier to participation at selective universities for students from disadvantaged backgrounds is low attainment at school," he added.