The proportion of students in England awarded first-class degrees continues to increase - rising by 80% since 2010-11, the university watchdog says.
The Office for Students, warning of grade inflation, says for almost three-quarters of universities such increases in top grades are "unexplained".
The University of Surrey increased its proportion awarded first-class degrees from 23% to 47% of students.
Education Secretary Damian Hinds warned against "unfair practices".
"Worries about grade inflation threaten to devalue a university education in the eyes of employers and potential students," said Susan Lapworth, director of competition for the Office for Students.
The higher education watchdog also examined why the proportion awarded top degrees might have risen from 16% to 29%, such as students arriving from school with better qualifications.
But the analysis found much of the increase could not be explained.
The figures showed over 40,000 more students graduated with firsts last summer than in the cohort of seven years before.
Mr Hinds said that if universities were giving many more top degrees without a legitimate reason, it was unfair on those who had studied to the same standard in previous years.
"We owe it to the hard-working students and institutions who play by the rules to stamp out this unfair practice. Today's figures are disappointing and risk compromising the public trust in the high standards of our universities," said the education secretary.
The watchdog showed the changes in students awarded first-class degrees between 2010-11 and 2017-18, including:
l Imperial College London from 31% to 46%
l University of Huddersfield: 15% to 40%
l University College London: 24% to 40%
l Durham University: 18% to 38%
l University of East Anglia: 14% to 39%
l University of Northumbria: 16% to 35%
l University of West London: 13% to 34%
l Staffordshire University: 14% to 34%
The study also looked at those awarded either first or upper-second class degrees (2:1s). These now account for the great majority of degrees.
In the University of Bristol, 92% of students are awarded either a first or 2:1 and at Cambridge 94% reach this threshold.
Meanwhile, record numbers of 18-year-olds in England have applied for a place at university, figures from Ucas reveal.
The admissions service statistics show 236,350 school leavers - 40% in total - had applied by this year's deadline of 30 June - 3,970 more than in 2018.
This comes as a government review recommended cutting tuition fees in England from £9,250 to £7,500.
Across the UK as a whole, 275,520 young people have applied to university this year - up from 272,910 at the same point in 2018, but down from 278,130 in 2017.
The figures also show that there are record numbers of black, Asian and mixed race 18-year-old applicants, while the number of white applicants continues to fall.
Despite uncertainty over Brexit, the number of applicants, across all age groups, from the European Union has risen by 540 from 50,120 in 2018 to 50,660 this year.
The Ucas figures also show a record number of applicants from outside the EU applying to UK universities - 81,340 students have applied to study in the UK, an increase of 8%.
England's universities minister Chris Skidmore said it was "fantastic" to see record rates of 18-year-olds applying to university, "along with increasing numbers of applications from international students too".
