The UK boasts nearly one in 10 of the top 800 institutions in this year's World University Rankings.
The University of Oxford is in second place in the Times Higher Education's latest global league table, while the University of Cambridge and Imperial College London also make the top 10 in fourth and eighth places respectively.
The UK has seen an improvement on last year's results, but it also came with a warning that its long-term performance could be affected by continued cuts in higher education funding and immigration measures causing difficulties for overseas students.
UK institutions have the second highest proportion of international students among the top 200.
The 12th edition of the rankings sees the UK with 78 universities in the top 800, making it second only to the United States.
The university rated number one in the world is California Institute of Technology for the fifth year in a row.
London mayor Boris Johnson said he was "incredibly proud" to see four of the capital's universities in the top 30, its best performance to date.
The UK also has 34 institutions in the top 200, an improvement on last year's 29.
It sees Cardiff University and Queen's University Belfast both make their first appearance, while the University of Reading, University of Dundee and Newcastle University appear after losing their top 200 positions last year.
The majority of UK universities have moved up the rankings this year, some - such as the University of Warwick, University of St Andrews and the University of Exeter - considerably so.
But five - the University of Manchester, University of York, University of Leeds, University of Sussex and Royal Holloway, University of London - have slipped down.
Phil Baty, editor of the Times Higher Education World University Rankings, said: "The United Kingdom is a stand-out performer in this year's rankings, boasting an impressive 78 institutions overall, with 34 of these sitting in the top 200.
"The University of Oxford, the highest-ranked UK institution, is world number two.
"It appears the UK's position in the rankings has benefited from the fact that the country's research excellence framework (REF) assessment took place in the middle of the World University Ranking's period of assessment.
"It will be no coincidence that many of the top universities in the REF - University College London, King's College London, Imperial College London and the universities of Oxford and Cambridge - are also star performers in this list.
"However, despite the UK's success, its continued cuts in higher education funding - the Higher Education Funding Council for England received a £150 million budget slash this year - and series of immigration measures affecting overseas students, will hinder its performance in the long run.
"Many of the country's European rivals, such as Germany, Switzerland and the Netherlands, are also performing well, but are less hindered by funding cuts and more welcoming for international students.
"The UK will have to work hard to ensure its higher education spending and immigration policies do not hinder its place in the World University Rankings."
Twenty-nine new countries have entries this year, including Indonesia, Ghana, Nigeria, Bangladesh, Latvia, Qatar and Ukraine.
While the US remains the world leader when it comes to elite universities, its dominance has been eroded this year, with six of the top 10 universities compared to seven last year, and 39 of the top 100 compared to 45 last year.
There are more European universities in the world top 200 than ever before, while there was a more mixed picture for Asia, with Japan and South Korea falling back this year and China remaining steady.
Nevertheless, Japan is in third place of universities represented overall, with 41 appearing in the top 800, while China has 37, Korea and Taiwan both have 24, and India has 17.
Mr Baty said the rankings "apply rigorous standards, using tough global benchmarks across all of a global research university's key missions - teaching, research, knowledge transfer and international outlook".
"The top 800 list represents just 4% of the world's higher education institutions, so we congratulate all institutions who have made this year's list."
Mr Johnson said: "I'm incredibly proud that four of London's universities are in the top 30 worldwide according to this survey. The capital continues to be the global leader in education, innovating and inspiring top talent from both across the country and overseas."
Universities Minister Jo Johnson said: "It is great to see the UK is second only to the US for the number of world-class universities in the top 80.
"These rankings confirm the world-class standing of our higher education sector. Our reforms will ensure our universities continue to compete with the very best internationally and deliver high-quality teaching to students at home."
Nicola Dandridge, chief executive of Universities UK, said: "This table, and other rankings, suggest that the UK continues to possess, by some margin, one of the strongest university systems in the world.
"What is clear, however, is that if we want to maintain this leading position, we must start matching our competitors' increased investment in higher education. We should also be presenting a welcoming climate for genuine international students and academics and ensuring that visa and immigration rules and procedures are proportionate."