Pupils who have private tuition achieve on average just half a grade higher in their maths and English exams than those who have had no extra tuition, research from London University’s institute of education shows.

Academics found boys increased their performance by three-quarters of a grade in maths, often sufficient to push them up a grade. But maths tuition was shown to have little effect on girls’ performance.

There was no evidence that out-of-school coaching in English had any effect on exam grades, for either boys or girls. Twenty-seven per cent of the 300 16-year-old pupils surveyed by academics admitted using a private tutor at some point during their schooling, usually in maths or English.

The study’s authors suggested that a lack of confidence among the girls led them to seek coaching when in fact their grades did not need to be improved. A general improvement in girls’ performance between the ages of 14 and 16 also makes it more difficult for tutors to boost results.

Judith Ireson, professor of psychology in education and co-author of the report, said previous research showed coaching offered by schools raised grades.

“Most people assume tutoring is the answer to boosting children’s attainment,” she said. “But there is no regulation of private tutors, so there is no guarantee that the tutor you get is going to be good.”

The Prime Minister is among many parents who believe private tuition, which costs on average pound;20 an hour, reaps benefits. Tony Blair hired teachers from Westminster school, one of the UK’s highest-achieving private schools, to tutor his eldest children.

Clive West, the director of private-tuition agency Anysubject, said:

“Parents are not dim-witted. They do not come back to us without reason.”

Mapping and evaluating shadow education, by Judith Ireson and Katie Rushforth, is available on: www.ioe.ac.uk