At the University of East London, the projected drop-out rate, based on the records of undergraduates in recent years, is 36 per cent compared with just one per cent at Cambridge. Overall, nearly one in five students drops out - at a total cost to the taxpayer of around pounds 200m.
At a few universities, only just over half of those expected to get a degree at the end of three years do so. Baroness Blackstone, the higher education minister, said that high drop-out rates are "a potential waste of talent and an inefficient use of taxpayers' money".
Ministers are pressing universities to take more students from poor backgrounds but the figures produced by the Government's Higher Education Funding Council for England suggest that these students are most likely to drop out: universities with high drop-out rates are often those with the highest proportion of students from the lower classes.
The University of East London, which has the worst drop-out rate, takes 94 per cent of its pupils from state schools and 38 per cent from families in the lowest three social groupings.
Christine Hodgson, the director of communications at the University of East London, said students there don't follow the usual college career path. "We have people who come, then leave, don't come back or come back five years later: it's very difficult to track," she said.
"We are absolutely on message as far as the Government is concerned, but our drop out rates are absolutely linked to the circumstances from which our students come.
"There is a huge tradition in the East End of not going to university and we are having a lot of success," she said. "We have bright students, but they are rusty and they need extra support. They also need cash support. The current loan is dismal and people are put off applying because of the debt."
The National Union of Students also condemned the waste of money, but blamed drop-outs on a lack of government support for students. A spokesman said: "The overwhelming reason for people dropping out is financial hardship. We are wasting public money with students dropping out because the Government is not funding them properly."
Officials point out that students with the worst A-level scores - who tend to be those from poorer backgrounds - are those who are most likely to abandon courses.
The Higher Education Funding Council said that Britain had lower drop- out rates than in most competing countries: 37 per cent in the US; 45 per cent in France; and 66 per cent in Italy, though in Japan they are only 11 per cent.
Bahram Bekhradnia, the council's director of policy, said: "The great news is that despite doubling participation rates, there has been only slight increase in drop-out rate."
David Triesman, general secretary of the Association of University Teachers, warned that "leaders of the institutions where there are problems should consider their positions carefully."
Britain's leading universities remain largely middle-class preserves. Oxford has the lowest proportion of state school pupils at 47 per cent, but Bristol, the London School of Economics and Imperial College are only just above Cambridge, which has 52 per cent.
London's medical schools also have some of the highest concentrations of private school pupils.
Queen's University, Belfast has the highest proportion of state school entrants (97 per cent) while, in England, the universities of Central Lancashire, East London, Derby, Huddersfield, Sunderland and Wolverhampton all have 94 per cent.
n A jewellery collection inherited by Nuffield College, Oxford, nearly 40 years ago was sold at Sotheby's yesterday to raise money for hard-up students. The jewels of Lady Nuffield, who died in 1959, were passed on to the college founded by her husband after his death four years later.
The collection fetched a total of pounds 118,627, which will go towards a fund to help finance graduate students.