The Pisa tests, run by the Organisation for Economic Co-operation and Development, show the UK rising in reading, maths and science.
But the UK lags behind top performers such as China, Singapore and Estonia.
The UK's teenagers were also found to have among the lowest levels of "life satisfaction".
Andreas Schleicher, the OECD's education director, said there were "positive signals" from the UK's results for the tests taken in 2018 - which he said showed "modest improvements".
In reading, the UK is 14th, up from 22nd in the previous tests three years ago
In science, the UK is 14th, up from 15th
In maths, the UK is 18th up from 27th
The UK's maths results represent a particular improvement on three years ago, according to an analysis by the National Foundation for Educational Research (NFER).
But it says there has been no significant change for reading or science, with scores remaining broadly similar in Pisa tests since 2006, despite fluctuations in rankings.
This year's science score has shown a slight fall, in fact, but because other countries' results have also slipped, the UK has climbed upwards in the rankings.
At the current rate of progress, Mr Schleicher said, it would take a "very long time" for the UK to catch up with the highest achieving countries.
He suggested more investment in teachers' skills as a way to make improvements.
"Pupils in England have continued to perform well in reading and science and have made significant improvement in maths," said Carole Willis, chief executive of the NFER, which published an official analysis of the UK results.
But she called for more investigation into why "pupils in England were more likely to have negative feelings".
Geoff Barton, leader of the ASCL head teachers' union, warned during an election campaign there was a risk of "over-claiming or over-blaming" about these results.
But he said attention should be paid to the low levels of wellbeing and the "great pressure" experienced by teenagers.
Sir Peter Lampl, founder of the Sutton Trust social mobility charity, said: "We need to do more to narrow the gap between rich and poor students, particularly for the highest performing ones."
Education Secretary Gavin Williamson said the rise in the rankings reflected the efforts of Conservative governments to have "more rigorous primary school assessments and more pupils are now studying the core academic subjects at GCSE".
But Kevin Courtney, joint leader of the National Education Union, said it was too early to draw any conclusions about the Conservatives' changes to education from these results.
Paul Whiteman of the National Association of Head Teachers said teachers and school leaders deserved credit for the results "given the very difficult circumstances in which they have been forced to operate over the past 10 years".