US academics have produced international comparisons in key subjects - using tests taken in 2011 by 900,000 pupils in over 60 countries.
It shows that Northern Ireland is Europe's top performing education system for primary maths.
England has slipped in science, but is top 10 for primary and secondary maths.
The top places in this global education league table have been taken by Singapore, Hong Kong and South Korea. Finland is among the highest placed European countries.
Such comparisons have become increasingly influential - measuring pupils against the standards of international competitor countries.
Globalisation in the jobs market and the economy has seen education ministers wanting to benchmark pupils' achievement against current international rivals.
Such international rankings have also highlighted the educational strength underpinning the emerging economic powers in Asia.
These latest rankings bring together two major studies - the four-yearly Trends in International Mathematics and Science Study (TIMSS) and the five-yearly Progress in International Reading Literacy Study (PIRLS).
They reveal the continuing pattern of domination by a group of Asian education systems - South Korea, Singapore and Hong Kong (such international comparisons include regional school systems as well as countries).
But the study, compiled by researchers at Boston College in the US, shows that England and Northern Ireland are performing strongly in the following group of European education systems.
Source: TIMSS 2011
In maths, the study says England has been one of the most improved between 1995 and 2011. England remains in the global top 10 for maths - in 9th for primary and 10th for secondary.
England has slipped in primary science tests, taken by 600,000 10 year olds - down to 15th place from 7th place in the last tests in 2007. There was also a dip for secondary science, taken by 14 year olds, down from 5th to 9th place.
In the literacy tests, taken by a sample of 325,000 primary school pupils, there was progress for England - up from 15th to 11th.
A spokesman for Education Secretary Michael Gove said: "These tests reflect progress between 2006 and 2011 and were taken only a year after the election.
"So to the limited extent the results reflect the effect of political leadership, Labour deserves the praise for the small improvement in reading and the blame for the stagnation in maths and the decline in science. The tests say nothing, good or bad, about what we have done."
Labour's education spokesman, Stephen Twigg, said: "These results show schools in England are some of the best in Europe - thanks to the hard work of teachers and pupils. The Labour government's reforms saw reading results improve thanks to better teaching, smaller class sizes and Labour's National Literacy Strategy.
Source: TIMSS 2011
"However, we need to understand why East Asian countries out perform us in key skills - particularly science and maths."
Mr Twigg also highlighted the lower achievement for Sweden in reading - linking it to the free schools inspired by the Swedish education system.
There was a particularly strong performance for Northern Ireland - in 6th place for primary maths, which meant it was the highest ranking European school system.
Northern Ireland, taking part in these tests for the first time, is in 5th place for primary reading - in a top group alongside such education superpowers such as Finland and Hong Kong.
In terms of the proportion of pupils reaching the highest ability levels, Northern Ireland was even more successful, in 3rd place.
The maths study also ranked the "safe and orderly" levels of schools - and found Northern Ireland was at the top, with England in 14th place.
There was also a ranking of bullying for the primary maths study - with England having one of the worst records in Europe, in 30th place in terms of students' views of the levels of bullying.
Scotland and Wales did not take part in these rankings.
Such results show long-term trends, overlapping between different governments and education ministers. In England, the tests were taken under the current coalition government, but the pupils would have studied under the reforms of the previous Labour government.
Source: PIRLS 2011
Researchers say the factors linked to success are a supportive home background and schools which have good discipline and experienced and well-motivated teachers. They also mention negative social factors, such as too many older pupils having learning impaired by a lack of adequate sleep.
The maths study examined the availability of resources at home - such as books - with pupils in South Korea, Norway, Sweden and the US being the best equipped. Indonesia and Ghana had the least learning materials at home.
There is a broad pattern repeated across these tables, with a cluster of Asian, Pacific Rim, countries at the top, European and western countries in the upper and middle ranks, with countries in North Africa and the Middle East in the lower ranks.
Report author and Boston College professor, Michael Martin, said that the success of the top-performing countries reflects the long-term investment - and shows the way for other developing countries to follow.
"Education is a multi-generational enterprise," he said.
"One thing you can learn from these is what's possible. That comes as a shock sometimes, what students in other countries can actually do and the gap sometimes between what your students are achieving and what students in other countries are achieving," said Prof Martin.
There are other international rankings - but these also show a similar picture at the top of the table, with education systems such as South Korea, Hong Kong, Finland and England among the highest performers.
In global league tables assembled by Pearson last month, Finland and South Korea were top, with England in 6th place.
The less expected success of the TIMSS and PIRLS rankings will be the high performance of Russia, which has a place in all their top 10s.
Another prominent international ranking, the PISA tests run by the Organisation for Economic Co-operation and Development, has shown a strong performance for Chinese education systems, including Shanghai and Hong Kong.
Asian countries have taken top places in global school rankings for maths, science and reading, with England and Northern Ireland among high performers.