Cambridge and Oxford are among the most prestigious universities in the world, according to new international rankings, but other UK institutions are losing ground.
A new global league table shows that the two top universities remain part of an elite group of "super brands".
They were placed third and fourth respectively in the latest Times Higher Education (THE) World Reputation Rankings, with Oxford moving up two spots from sixth last year.
The rankings measure the power of university brands, based on the opinions of senior academics.
But researchers warned of a polarisation between the very top institutions in the UK, and the rest, amid increasing competition from Asian nations.
The UK has lost three universities from the top 100 in the last two years, the rankings show.
The latest table reveals that Leeds University has dropped out of the top 100, joining Sheffield University and the London School of Hygiene and Tropical Medicine, which lost their places last year.
Other UK universities, however, are faring better. Bristol University has clung on to a top 100 spot, at the bottom in the 91-100 group, while Manchester came 47th, putting it in the top 50 for the first time.
Edinburgh University - the only Scottish institution in the top 100 - rose three places to 46th.
University College London rose one place to 20th, and the London School of Economics increased four places from 29th to 25th.
Overall, the UK had nine universities in the top 100, compared to 12 two years ago.
Only the United States had more institutions into top 100 this year - 43 in total - with Harvard taking first place in the rankings, and Massachusetts Institute of Technology in second.
The magazine's rankings editor, Phil Baty, said there was some good news for the UK, but only for a handful of universities.
"Outside the chosen few, there is cause for alarm: the UK has lost three institutions from the world top 100 list since the reputation rankings were first published in 2011.
"Traditionally, the strength in depth of the UK system has been one of its great features. Having a large number of institutions with truly world-class standing has delivered huge returns for the whole sector and the wider economy.
"However, it now seems that a gap is opening up between the very best and the rest, with even household name institutions like Sheffield and Leeds losing their lustre and falling down the rankings."
Baty claimed that government attempts to introduce a market into higher education, and "concentrating increasingly scarce resources on a select few" means that there could be further trouble ahead for all but a small number of universities.
"It would be bad news indeed for UK plc if the bulk of the UK's world-class universities are relegated to the global lower leagues," he added.
The latest rankings show that a number of leading Asian institutions are rising up the table.
The National University of Singapore has gone from 23rd to 22nd place, Seoul National University in South Korea is now in the top 50, the University of Hong Kong is 36th, up from 39th last year and the National Taiwan University is now in the 51-60 group, compared to the 81-90 group in 2011.
Australia has also moved ahead, with six institutions in the top 100 this year, compared to four last year.
Baty said that no university can be complacent about its position.
"New forces in higher education are emerging, especially in the East Asian countries that are investing heavily in building world-class universities, so the traditional elite must be very careful," he said.
"In the three years that the World Reputation Rankings have been running, we have clear evidence that the US and the UK in particular are losing ground."
The top 10 universities in terms of reputation, with last year's rankings in brackets, are:
1. (1) Harvard University
2. (2) Massachusetts Institute of Technology
3. (3) University of Cambridge
4. (6) University of Oxford
5. (5) University of California, Berkeley
6. (4) Stanford University
7. (7) Princeton University
8. (9) University of California, Los Angeles
9. (8) University of Tokyo
10. (10) Yale University
Dr Wendy Piatt, director general of the Russell Group, which represents 24 leading universities, said: "All league tables have their limitations and students should look beyond them when picking a degree course. The global reputation of the UK's leading universities remains strong with seven ranked in the top 50 worldwide and overall we come second only to the United States.
"Our universities punch well above their weight and do more with less, outperforming most rivals relative to expenditure. But if the UK is to remain a global leader in higher education, with truly world-class institutions, then the Government must concentrate investment where it will have the most impact."
Nicola Dandridge, chief executive of vice-chancellors' group Universities UK, said: "These tables, and other rankings, show that the UK continues to possess the second-strongest university system in the world after the US.
"The UK attracts more overseas students per capita than the majority of major higher education systems, and we remain one of the world's leading research powers measured by total publications and citations.
"Of course, reputation is very subjective and such tables cannot tell the whole story about the strength of our system. Universities' positions will vary from one league table to the next and this is just a small snapshot of our sector."
A spokesman for the Department for Business, Innovation and Skills (BIS) said: "The UK has a global reputation for excellence in higher education. We have strong institutions, a world-class research base and dedicated staff.
"To stay ahead in the global race, we are protecting the research budget, making UK research more accessible and delivering a better student experience."
Shadow universities minister Shabana Mahmood said: "Despite UK universities continuing to show their relative strength on the world stage, it is important to understand why universities in other countries are gaining ground compared with Britain.
"There are now fewer UK universities in the world's top 100 this year compared to last year and the year before. This downward trend should give ministers cause for concern because on their watch, it now seems the international standing of UK universities is starting to fall.
"With other nations around the world investing heavily in higher education with governments that are more welcoming to legitimate international students, the Government should take a long hard look at its policies."