Edinburgh and King's College London have edged into the top 20 of the QS World University rankings.
Cambridge, UCL, Imperial and Oxford all made it into the top 10.
But John O'Leary, of QS, warned that unless the UK puts more funding into higher education its leading position could slip.
The top UK university was Cambridge in third position, behind Massachusetts Institute of Technology at the top of the table and Harvard in second.
University College London (UCL) and Imperial occupied fourth and fifth places, with Oxford in sixth.
Universities in the United States made up the rest of the top 10.
There were eight UK universities in the top 50 and 18 in the top 100, with graduates from Oxford and Cambridge rated as the world's most employable by 27,000 global graduate employers polled for the ranking.
"Clearly the prestige of a UK degree is recognised by employers around the world, and the brand-name value of Oxbridge has so far survived any negative publicity following the tuition fee hikes and student protests," said Ben Sowter, head of research at QS.
However the rankings also suggest that UK universities struggle to keep up with the US when it comes to cutting-edge research.
Of UK universities, only Cambridge made the top 30 for research citations, with UCL, Oxford and Imperial in the top 50.
"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."
UCL's new president and provost, Professor Michael Arthur, said the university's high place in the rankings reflected its efforts both in the UK and overseas.
But he said: "As pleasing as it is, rankings success will not divert us from focusing on our core mission of educating and inspiring our students and delivering world class research."
Dr Wendy Piatt of the Russell Group noted that all six UK universities in the top 20 and 17 of the 18 in the top 100 were members of the group.
"Their focus on research excellence and high-quality teaching means the UK performs formidably well against other nations in spite of its size", said Dr Piatt.
However, she warned: "If our universities are to compete in the future they need the government to provide light-touch regulation and continued investment, and to be welcoming to genuine international students.
"It is worth again highlighting that the process of ranking universities is fraught with difficulties and they should not be used alone in judging the quality of an institution."
Top 20 universities
1. Massachusetts Institute of Technology (MIT)
2. Harvard University
3. University of Cambridge
4. University College London (UCL)
5. Imperial College London
6. University of Oxford
7. Stanford University
8. Yale University
9. University of Chicago
10. California Institute of Technology (Caltech)
11. Princeton University
12. Eth Zurich (Swiss Federal Institute of Technology)
13. University of Pennsylvania
14. Columbia University
15. Cornell University
16. Johns Hopkins University
17. University of Edinburgh
17. University of Toronto
19. Ecole Polytechnique Fédérale de Lausanne
20. King's College London
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- Unknown Updated at: Tuesday, September 10, 2013
