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10 September 2013, 09:17 | Updated: 30 March 2016, 13:50
The University of Southampton's been named in the world's top 100.
It's been placed at 86, while four of the world's best 10 universities are in the UK, according to the new international table.
A record six British institutions have made it into the top 20 in the latest annual QS World University Rankings.
But experts warned that the UK's leading position could be under threat without more funding.
The top-ranked UK university is Cambridge, which has slipped down a place to third this year, behind Massachusetts Institute of Technology - which was also first last year - and Harvard, both leading US universities.
Also in the top 10 were University College London (UCL) in fourth place, Imperial College London in fifth, and Oxford in sixth.
The other institutions in the top 10 were all in the United States.
Edinburgh and King's College London both moved up into the top 20 in 17th and 19th place respectively.
There were eight UK universities in the top 50 and 18 in the top 100.
QS head of research Ben Sowter said the prestige of a UK degree is recognised by employers around the world.
The authors said that of the 45 British institutions in top 400, 29 rank lower than they did at the time of the economic crisis in 2008/09.
Since the recession, 21 institutions in the UK have dropped by more than 10 places in the rankings, while five are now 10 places higher than in 2007.
Cambridge was the only UK university to make the global top 30 for research, with UCL, Oxford and Imperial making it into the top 50. This suggests that the UK is struggling to keep up with the US in producing cutting-edge research, the authors said.
John O'Leary, member of the QS Global Academic Advisory Board, said:
"The UK invests below the Organisation for Economic Co-operation and Development (OECD) average in higher education, so it is unrealistic to expect its universities to continue to punch above their weight indefinitely.
"The current success of leading institutions shows how vital it is that the Government matches the investments being made by other countries in order to maintain their world-class status.''
Universities minister David Willetts said the results were "fantastic news'' and that UK universities are world-class.
"We are not complacent, and we know we must work hard to remain the best. Our reforms to undergraduate finance have put universities on a sustainable financial footing and sharpened incentives to deliver a world-class student experience.''
The UK universities in the top 100 are: Cambridge (3), University College London (4), Imperial College London (5), Oxford (6), Edinburgh (17), King's College London (19), Bristol (30), Manchester (33), Glasgow (51), Birmingham (62), Warwick (64), London School of Economics and Political Science (68), Sheffield (71), Nottingham (75), St Andrews (83), Southampton (86), Durham (90) and Leeds (97).