Supporters of the specialist schools programme, which now accounts for about two-thirds of schools, said the findings justified the millions spent on the scheme since its launch in the early 1990s.

Professor David Jesson of York university and David Crossley of the Specialist Schools and Academies Trust, which commissioned the study, analysed GCSE papers taken last summer. They said the average key stage 2 point-count of pupils entering specialist schools was 27.1, meaning 56.4 per cent should have left with five good GCSEs. In fact, 58 per cent made the grade.

Pupils at 14 academies - independent state schools that are an offshoot of the specialist programme - achieved at an even faster rate: 35.5 per cent got five good grades, compared with the predicted 29.5 per cent.

By comparison, pupils at non-specialist schools saw their results slide.

The study found that 49.7 per cent were predicted to achieve at least five A*-C grades, based on their ability at KS2, but the actual figure was 46.7 per cent.

Harvey Goldstein, professor of social statistics at Bristol university, said the conclusions could be oversimplistic. He said they fail to take into account pupils moving into specialist schools at a later age and the fact that some specialists can select a proportion of their pupils.

He said:“There are a lot of pitfalls in this kind of analysis. You have to be cautious when drawing strong conclusions from it.”

But Sir Cyril Taylor, chairman of the trust, said: “This report confirms what we already know - that specialist schools are making a huge contribution to raising educational standards and are having a positive impact on the millions of students who pass through them.”