Report suggests it is affluence, not better teaching, that is behind the results gap.
Private schools do no better than their state counterparts once the backgrounds of their pupils are taken into account, according to a respected international study.
Children educated at independent schools gain higher exam results because they are surrounded by other privileged pupils not because the schools are themselves any better, the report by the Organisation for Economic Co-operation and Development found.
The Programme for International Student Assessment (Pisa) examines the performance of 250,000 15-year-olds in 41 countries in tests of their reading, mathematics and science skills.
Finland was the top performing country, placed first in reading and science and second in maths. Hong Kong was first in maths.
The UK was not included in the latest international comparisons because its data did not reach the standard required by the OECD, a think-tank based in Paris.
When the first study was published three years ago, the UK rated eighth on maths, seventh on reading and fourth on science. Data collected for the UK for the latest study would have placed the UK 11th in science, 12th in reading and 18th in maths.
Unlike many other studies, Pisa is designed to test how well students are prepared for adult life rather than their understanding of the curriculum.
Critics suggest the UK government may have been happy to see its results excluded.
Professor Alan Smithers, director of the centre for education and employment research at Buckingham university, said: "There is hardly any difference between our response rate this time and last time. Results this time are more in line with previous studies. That will be embarrassing for ministers because they made an awful lot of the results last time."
The OECD insists not enough pupils in participating schools completed the tests and that it was their decision not to publish the UK's results alongside those of other countries.
An analysis of maths test scores - the prime focus of the second Pisa report - found schools with a high concentration of pupils from well-off families benefit from a "peer effect" which increases the advantages of already privileged children. They also enjoy improved discipline and find it easier to attract good staff.
"Private schools may realise a significant part of their advantage not only from the socio-economic advantage that students bring with them, but even more so because their combined socio-economic intake allows them to create an environment that is more conducive to learning," the report said.
It also suggested that UK private schools are among the most elitist in the world.
The report also found countries with selective systems were more likely to have wide differences between the attainment of pupils.
To improve attainment in countries such as the UK where social class is closely linked to under-performance policies are needed to target at-risk pupils.
John Bangs, National Union of Teachers' head of education, said: "This is the equivalent of the Government not submitting their league table results.
"The message from Pisa is that the issue for policy makers is social class, social class, social class."
Analysis 14 Learning for tomorrow's world: First Results from PISA 2003 is available at www.oecd.org