The University of Sheffield was named as the 110th best university in the world, up from joint 121st last year. The University of Leeds rose more than 30 places from joint 160th to joint 127th, and the University of York dropped a similar number, from joint 133rd to 169th.
The University of Oxford became the first institution to retain top place in an international league table for the sixth year in a row.
A number of UK universities have climbed the Times Higher Education world rankings – with Cambridge rising from sixth to fifth place and the University of Manchester moving into the top 50.
Overall, the UK has 28 universities in the top 200, down from 29 last year.
Of these, more than half (15 institutions) have improved their ranking, four universities have stayed the same, and nine institutions have dropped by at least one place in the past 12 months.
Experts have warned that Covid-19 and Brexit have provided “new challenges” for UK universities.
They say British institutions will have to “work hard” to attract international students and academic talent in order to retain its position as a “higher education superpower” amid increasing global competition.
The annual list rates more than 1,600 universities from 99 countries and regions in five areas: teaching, research, citations, international outlook and industry income.
The rankings show Oxford was named the best-performing university globally, ahead of California Institute of Technology and Harvard University in the United States, which both took second place.
US universities dominated the top 10 in the rankings, claiming eight places for the second year in a row.
Stanford University in the US came fourth, while the University of Cambridge and Massachusetts Institute of Technology (MIT) both took fifth place.
Imperial College London took 12th place compared to 11th last year, while University College London (UCL) fell from 16th place to joint 18th place.
Phil Baty, chief knowledge officer at Times Higher Education, said: “Although the UK has seen some good results this year, Covid-19 has provided new challenges to add to those related to the impact of Brexit.
“These challenges mean the UK must work hard to attract international students and academic talent to contribute to its knowledge economy in both the short and long-term.
“With mainland China and Germany rising, this will be essential for the UK to retain its position as a higher education superpower.”
Professor Louise Richardson, vice-chancellor of the University of Oxford, said: “My colleagues and I are absolutely delighted to have achieved the top ranking again. There are many great universities around the world and we are proud to be in their company.
“This past year has demonstrated to our publics, our governments, and even to ourselves just how much universities can contribute to society.
“The vaccine Oxford developed is being distributed in over 170 countries and over a billion doses have been manufactured.
“Together our universities have made the strongest possible case for renewed public investment in research universities.”
Here is the list of the UK universities in the top 200 of the latest THE World University Rankings. Last year’s positions are in brackets, while = denotes joint position.
– 1 (1) University of Oxford
– =5 (6) University of Cambridge
– 12 (11) Imperial College London
– =18 (16) University College London
– 27 (27) London School of Economics and Political Science
– =30 (30) University of Edinburgh
– =35 (35) King’s College London
– 50 (=51) University of Manchester
– =78 (77) University of Warwick
– =86 (=92) University of Glasgow
– 92 (91) University of Bristol
– =105 (=107) University of Birmingham
– 110 (=121) University of Sheffield
– =117 (110) Queen Mary, University of London
– =122 (=136) Lancaster University
– 124 (=127) University of Southampton
– =127 (=160) University of Leeds
– 141 (=158) University of Nottingham
– =143 (=174) University of Exeter
– =146 (=178) Newcastle University
– =151 (=160) University of Sussex
– =158 (=178) University of Aberdeen
– =162 (=149) Durham University
– 169 (=133) University of York
– =178 (163) University of Liverpool
– 182 (=200) University of East Anglia
– =185 (=170) University of Leicester
– 189 (=191) Cardiff University