Heads and senior staff from 80 schools will hear how a project at Pate’s grammar school in Cheltenham - one of the top state schools in the country - has doubled the number of successful applicants from the local, deprived area. The scheme has also been praised by evaluators from Oxford Brookes University for boosting the self-esteem and self-confidence of the children taking part, improving their cooperative skills and making them more responsible.

But any attempts by other grammars to win government funding for similar schemes may fall foul of ministers’ opposition to selection.

The Crypt school in Gloucester has applied for money to run such an enrichment project under the Excellence in Cities programme for gifted and talented children but has not yet heard the result. The Department for Education and Skills said any bid would be assessed on its merits.

“We support non-selective and selective schools working together to raise standards for all children in all schools but that is not the same as selective schools using these programmes to entrench selection,” a DfES spokesperson said.

Under the pound;40,000-a-year project at Pate’s, sponsored by the Sutton Trust, 65 talented 10-year-olds visit for one afternoon a week. Activities, such as producing a magazine on homelessness, take place in a specially designed classroom and are led by Sharon Johnson, a former deputy primary head.

Since the scheme was introduced, the number of successful applicants from local primaries has shot up from 10 to 20 in a single year, out of a total intake of 120.

Now the Sutton Trust is offering the scheme as a nationwide model for the other 160 grammar schools. This and other outreach schemes will be discussed at a conference in London organised by the Specialist Schools Trust and the Sutton Trust, whose chairman Sir Peter Lampl is a former Pate’s pupil.