A scheme that is offering free private tuition to London state school pupils this term could be expanded nationally with new Government funding.

The Sutton Trust pilot project has just started in 10 secondaries serving disadvantaged areas of the capital.

It aims to test whether personal tuition, bought by increasing numbers of wealthier families, can improve the GCSE results of less privileged pupils.

Now Sir Peter Lampl, chairman and founder of the trust, has identified the scheme as a candidate for expansion through the Education Endowment Fund (EEF), a pound;125 million pot of Government money his charity is overseeing.

“We have a bunch of kids doing GCSE maths who are receiving private tuition and a bunch of kids who aren’t,” he said. “We are going to see how effective private tuition really is.”

Sir Peter said he thought one-on-four tuition might work as well as one- on-one sessions and that he found the idea of combining them with computer-based tutoring “very, very interesting”. The initial pilot is using tutors from a London agency.

The fund is inspired by President Obama’s Race to the Top programme which uses a competition for grants to encourage school reform.