The study, by Ian McCallum, the former principal research officer at the London Research Centre, shows that local education authorities with the lowest proportion of household heads in partly skilled or unskilled occupations are those with the best key stage 2 skills.
The research, which looks at primary pupil performance in the London boroughs, comes at a time when Tory ministers have sought to blame council mismanagement for low standards in many areas.
This week the Prime Minister John Major returned to the attack, claiming the 20 bottom-performing LEAs in the national league tables for primary tests were all Labour.
The research fuels the debate over the extent to which poverty and social backgound excuse poor school results. In February, Labour embraced the principle of "zero tolerance of failure" in education, when the party's literacy task-force claimed there was an "unacceptable" gap in achievement,irrespective of wealth or poverty.
The party, however, recognises that social factors do have a part to play - a belief that underpins its plans to set up action zones to raise standards in inner-city areas.
But while demonstrating the importance of social class as an indicator of performance, Dr McCallum lends support to Labour's claims that boroughs with similar social characteristics can achieve significant ly different results.
Dr McCallum's research compares last month's key stage 2 league table results with the information on social class taken from the 1991 Census.
Richmond, Bromley, Kingston, and Kensington and Chelsea top the list for key stage 2 performance and have the lowest percentage of heads of household in partly skilled or unskilled occupations.
Barking, Tower Hamlets, Hackney and Newham are at the bottom of the league table and have the highest percentage of heads of household in partly skilled or unskilled occupations.
The research also shows that 15 London boroughs are performing better than would be expected given their social complexion: 16 are below and one is right on target.
Some of the LEAs at the bottom of the table are actually doing better than those at the top, given their social class.
The achievement in Barking, for example, which is at the bottom of the national league table, was almost as great as that at Richmond, which is the country's top-performing LEA at key stage 2.
The research fuels the debate over the extent to which poverty determines educational performance, with Labour now agreeing with the Government that other factors may be even more important.
The party's literacy task-force, chaired by Professor Michael Barber, compared figures for key stage 2 test results with the proportion of children given free school meals - a key poverty indicator.
It found that even in the most disadvantaged schools, where more than 40 per cent of children were given free meals, there was a range from 70 per cent to zero of pupils achieving the national target. It concludes: "Whether children learn to read well is a lottery in both advantaged and disadvantaged areas."
Dr McCallum said his research should be studied carefully by politicians of all parties.
He said the census data provided important additional indicators of factors likely to be associated with the ways in which parents are able to provide their children with educational support. No account was taken in Dr McCallum's research of the percentage of children with English as a second language.
But he said: "In spite of the lack of more detailed evidence about individual pupils and the characteri stics of LEA provision, the evidence is overwhelming that factors other than the political complexion of the LEA play the major part in determining how well pupils perform."
Dr McCallum claimed that just 20 per cent of differences in pupil performance in London LEAs could be attributed to other variables, which were independent of social class.
Chris Waterman, education officer with the Association of London Government, said: "We've argued consistently for more sophisticated measures of performance than raw results. These figures show the need for a more sensitive and realistic appraisal of school performance."