Cambridge and Oxford remain in the top five, at fourth and fifth place respectively, but both have moved down two places on their 2015 ranking.
The US continues to dominate the Times Higher Education (THE) world reputation rankings, with Harvard top.
Asia has 17 universities in the top 100 - up from 10 in last year's rankings.
Three London universities stay in the top third of the table - Imperial College London at 15, University College London at 20 and the London School of Economics and Political Science at 24 - but each has fallen slightly on last year's ranking.
University of Edinburgh (38th), King's College London (43rd), University of Manchester (joint 49th), London Business School (between 81st and 90th) and University of Warwick (between 81st and 90th) also made the top 100 global reputation ranking.
London Business School was the only UK institution that improved its ranking; Edinburgh, King's and Manchester slipped down from their 2015 ranking, while Warwick stayed the same.
The University of Bristol and Durham University have fallen out of the top 100, bringing the UK's total number of universities in the rankings to 10 for 2016 - down from 12 last year.
The rankings are based on an invitation-only survey of leading academics.
The 10 top institutions by reputation are:
Harvard University, US
Massachusetts Institute of Technology, US
Stanford University, US
University of Cambridge, UK
University of Oxford, UK
University of California, Berkeley, US
Princeton University, US
Yale University, US
Columbia University, US
California Institute of Technology, US
'Diminishing performance'
THE rankings editor Phil Baty said the UK had lost ground this year.
"Even the country's most prestigious institutions have slipped, with the universities of Cambridge and Oxford each dropping two places to fourth and fifth place respectively," he said.
"The UK's diminishing performance occurs as institutions in Asia rapidly rise up the table - the continent has 17 representatives, up from 10 last year."
Mr Baty said cuts to higher education funding and a series of immigration measures affecting overseas students were "starting to have an impact" on the UK's global reputation.
"The UK will have to ensure that it can still draw in talent and investment from across the world and it does not lose its position at the heart of higher education's global elite," he added.
'Asia snapping at heels'
Dr Wendy Piatt, director general of the Russell Group of leading universities, said the UK had some of the very best universities in the world, but it was "no time to rest on our laurels".
"These rankings can be seen as a warning that the rest of the world is catching up with us and Asian universities, in particular, are snapping at our heels.
"We risk losing out on further business and overseas funding unless there is greater investment in our world-class universities and a more risk-based, proportionate approach to regulation.
"Our key international competitors recognise that world-class universities are central to their success."
