Oxford was top of the list for the highest average score for each of its researchers in the exercise, but it entered a smaller proportion of dons.
The London School of Economics produced its own league table to show that if Cambridge's decision to enter 98 per cent of dons were taken into account, it would come top. In the same table the London School of Economics was second and Oxford, which entered 91 per cent of its dons, third.
The assessment of 50,000 academics' research will be used to distribute pounds 700m to university departments next year. Those with the lowest ratings will receive no money from the Higher Education Funding Council's research budgets.
A spokeswoman for Cambridge said they were pleased with the results: "In many ways, we have done better than Oxford. It depends how you look at the figures. We have encouraged heads of department to put in as many people as possible."
But a spokeswoman for Oxford said: "We are quite happy about the way in which we put our entry together. Our figures hold up pretty well. We are very pleased the results of the exercise confirm the range and strength of Oxford's research and the international standing of the university."
Universities were allowed to choose what proportion of academics they entered for the exercise but those not included will not be eligible for funding. Some put prestige before funding.
Warwick, which came fourth in the LSE table, pointed out that only two other universities beside itself - Cambridge and the LSE - submitted almost all their staff.
The old universities dominated the top places, as they did when the last exercise was carried out four years ago. Among provincial universities, Bath and Warwick did best. But the new universities, which were polytechnics until four years ago, improved their performance, with an increase in the number of departments reaching the grades at which most work must be of national excellence from 96 to 351.
The new universities of Westminster, Portsmouth, Thames Valley, East London and Liverpool John Moores received top grades for some work. Sheffield Hallam had the highest rating of the new universities.
In traditional universities, the number of departments reaching standards of international excellence in at least some areas increased sharply.
Professor Brian Fender, the funding council's chief executive, said: "International excellence is not concentrated in tiny numbers of universities and colleges. The best universities have improved their international standing. Many other institutions have also performed impressively by identifying and building on their strengths."
The Funding Council meets next month to decide how to distribute research funds. It already concentrates most research money on a comparatively small number of universities.
Gillian Shephard, the Secretary of State for Education, has suggested the concentration might increase.
But Professor Fender said the aim was for the country to fund the best possible research for the money: "If it turns out that we could fund that better by a more concentrated distribution than is the case at the moment then why not? But the evidence doesn't point in that direction."
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