Wealthy families who use private tutors to help secure grammar school places should be taxed to help pay for poorer children to access the same help, it has been suggested.

The authors of a new study argue that a levy should be imposed on high-income families to help level the playing field in access to selective schools.

The paper, by academics at the UCL Institute of Education, examined the backgrounds of more than 1,800 children living in areas of England and Northern Ireland that have grammar schools.

It found that in England, poorer children - those from families in the bottom quarter of household incomes - had less than a 10 per cent chance of attending a grammar school, compared with a 40 per cent chance among those youngsters from families in the top quarter of household incomes.

Just under three-quarters of those children in England who were tutored gained a grammar school place, compared with 14 per cent of those that were not tutored, the report concludes.

Study author John Jerrim said: “The government claims that expanding grammars will boost social mobility. But our research shows that private tuition used by high-income families gives them a big advantage in getting in.

“The government, therefore, needs to explain how they are going to level the playing field between different income groups.”

He suggests that one option may be an extra tax for those who use tutoring services.

“I would envisage this as being levied on high-income families who use these services,” Prof Jerrim said, adding it could be seen as VAT-style tax.

The money could be distributed among lower-income families, for example to help provide free or subsidised extra tutoring for children from these backgrounds.

Controversial proposals to lift the ban on creating new grammar schools were a key plank of the Conservative manifesto in last year’s snap general election, but the plans were dropped in the wake of the election result, which saw the Tories lose their overall majority.

But grammars can still take on more pupils under rules that allow good state schools to expand.

A Department for Education spokesperson said: “We want every child to have access to a good school place and grammar schools are part of the choice available for parents.

“Research shows that pupils from disadvantaged backgrounds attain better results in selective schools, and around 60 per cent of these schools already prioritise children who are eligible for the pupil premium in their admissions - as recently as 2014, none of these schools were doing this.

“But there is more to do, which is why we continue to work closely with the sector to encourage schools to widen access for disadvantaged pupils.”