Free tuition should be given to bright children from poorer backgrounds to help them pass the 11-plus, according to a report warning grammar schools are increasingly monopolised by better-off families.

The Sutton Trust says the remaining 164 grammar schools in the country - of which 33 are in Kent - have proportionally more children from fee-paying prep schools than those on free school meals.

The study says radical steps are needed to ensure poorer brighter pupils have the opportunity to go to a grammar school.

It recommends that at least 10 hours free or subsidised tuition should be provided to applicants to create a level playing field.

It also urges grammars to give preference to children who are entitled to the pupil premium and says the 11-plus exam should be made less "coachable".

Kent County Council recently unveiled changes to the test that it hopes will make it more "tutor-proof" and help counter the widespread coaching culture that has evolved, particularly in west Kent.

Sir Peter Lampil, chairman of the Sutton Trust, said: "The big challenge, particularly in those areas where a selective system prevails, remains how to ensure that those grammar schools are open to all, and are not simply the preserve of better off families who can afford private tutors or prep school fees."

In Kent, the number of children at grammars who are eligible for free school meals mirrors the national figure of 2.7%. Non-selective schools in selective authorities like Kent have about 18% of children eligible for free school meals.

Meanwhile, nearly 13% of entrants to grammars come from outside the state sector.

Liberal Democrat county councillor Martin Vye said: "There is a big issue of less opportunity for disadvantaged children. The number of children at grammars on free school meals is consistently smaller than in schools as a whole."

If the system was overhauled, it could be improved to help children from poorer backgrounds, he added.