The Trends in International Mathematics and Science Study (Timss) is a major four-yearly comparison of standards in primary and secondary schools. In tests in 2007, England's 10 and 14-year-olds were among the higher performers in more than 60 regions. But their enjoyment levels had fallen.
Scotland's pupils' highest position was 15th for primary school science.
Wales and Northern Ireland were not involved.
Compiled by researchers in the United States, Timss is regarded as an important benchmark for comparing standards in maths and science around the world.
As in 2003, the best results have been achieved by Pacific Rim countries, such as Singapore, Hong Kong, Taiwan and South Korea.
The results put England's pupils ahead of other European countries, including industrial competitors such as Germany and the traditional education powerhouses of Scandinavia.
They also put England ahead of the United States and Australia on each of the assessments used by the researchers.
The highest score is for secondary science, where England's 14-year-olds are ranked fifth. In the three other categories, England was in seventh place.
This is a significant improvement on the last round of tests. Although a lack of sufficient data saw some of England's results left out of the tables, the scores for maths would have placed the country at 10th and 18th for the primary and secondary levels.
The best result from the 2003 study for England was fifth place for primary science.
In Scotland, primary pupils were ranked 22nd for maths and 15th for science and secondary pupils were 23rd for science and 17th for maths.
England's Schools Minister Jim Knight saw the results as a vindication of the extra investment in schools and the impact of the numeracy strategy.
This intensive plan for raising maths standards was launched in primary schools in 1999 by Tony Blair and his education secretary David Blunkett.
This cohort of English teenagers, who have scored so highly, would have been aged six when the numeracy strategy was introduced. In that year's Timss rankings, England's secondary maths pupils were in 20th place.
'Flash and bang'
However, Mr Knight also noted another contradictory trend in the findings - that pupils seemed to be enjoying the subjects less than they were four years ago.
The study found that in relation to their high achievement, there were relatively low levels of enjoyment among pupils - with a 13 percentage point drop in positive attitudes towards primary science.
Among secondary pupils, researchers noted that despite the improvements in science results, there has been a 21 percentage point drop in positive attitudes.
In response, Mr Knight promised more "flash and bang to enthuse pupils".
"I am determined to make maths and science more exciting subjects to teach and learn, and I want every school to have access to the most innovative and effective teaching methods."
John Dunford, general secretary of the Association of School and College Leaders, said the improvement was a "tribute to the commitment of everyone working in education to raise standards".
Chris Keates of the NASUWT teachers' union says the results are a "welcome indicator of the continuing hard work and dedication of teachers in England. They continue to rise to the relentless calls to secure ever higher standards".
Mary Bousted of the ATL said that it showed "the doom-mongers who undersell English schools have been proved wrong".
But the Conservatives' children's spokesman, Michael Gove, said it showed England's pupils were in the "global second division" behind Asian countries.
"Parents will be worried that our maths performance is behind that of Kazakhstan," said Mr Gove.
The international study also throws up some information about the home lives of these pupils.
The number of English secondary pupils with more than 200 books in their homes has "decreased significantly" since 2003 - although it remains above the international average.
Computer and internet use, for both primary and secondary pupils, remains very high - with 95% of primary pupils having computers at home and 92% of secondary pupils connected to the internet at home.
By international comparisons, pupils in England have relatively small amounts of homework.
The Timss survey, run by Boston College in Massachusetts, is claimed as the largest assessment of international pupil achievement, with each country sampling 4,000 pupils in 150 schools
The survey includes major economic powers such as Germany and Italy, the United States and Japan, Scandinavian countries and a range from eastern Europe, North Africa, the Middle East and Asia.
As well as national level results for the United States, it also includes findings from individual states and provinces in the US and Canada.