Dr John Marks, a member of the School Curriculum and Assessment Authority, used the results of last year's key stage 2 tests to write a report for the right-of-centre Social Market Foundation.
He found that in English the average pupil was 18 months behind the expected level of attainment, a gap which grew to two years in maths. According to the Department for Education and Employment a typical 11-year-old is expected to achieve level 4.
In English, 48 per cent of the year group had equalled or bettered what was expected of them, compared with 44 per cent in maths. One in eight pupils scored no better than seven-year-olds in English, a figure which rose to one in six for maths.
Dr Marks was particularly struck by the widely varying results he found between schools. The top 25 per cent of the nation's schools were ahead of the bottom 25 per cent by more than a year for English and 18 months in maths. And within the same education authority, pupils at the best schools were on average nearly four years ahead of the worst in English and five and a half years in maths.
However, the results have been attacked by the teaching unions who point out that they are based on data from the first full year of the tests.
The maths paper in particular caused problems, containing too many questions for the allotted time. Some schools gave extra time and will have scored more highly than those who did not, whose pupils will appear to have underperformed. Some schools taught to the tests and took them very seriously, while others did not.
Sheila Dainton, of the Association of Teachers and Lecturers' Policy Unit said that since the children involved had been taught entirely under the national curriculum its usefulness was called into question. She added: "We have grave reservations about the quality and validity of last year's tests and the dubious data upon which these results are based."
Dr Marks did not think his findings could be explained away by the way in which the tests were conducted. "I got more and more depressed. What I found was a shock, particularly the variation between one school and another. That really worried me, as did the differences across local education authorities. "
Eamonn O'Kane of the National Association of Schoolmasters Union of Women Teachers said that lambasting teachers would do no good but they would undoubtedly use the results of their own schools and classes to see where improvements were needed.
Education and Employment Secretary Gillian Shephard said that performance tables helped to lever up standards.