Lord Puttnam, chair of the General Teaching Council, told a conference that gifted children taught with older pupils could end up socially isolated. “It seems to me utterly self-defeating to simply transfer gifted children to classes of older pupils without being sure that we can also provide a rounded social environment.”

Lord Puttnam, who is also chair of the National Endowment for Science, Technology and the Arts, said there were dangers in sending young prodigies to university. Anyone attending Oxbridge at 12 was unlikely to emerge a rounded confident individual, he said.

Further criticism of ministers’ strategy for gifted children came from Deborah Eyre, head of the Research Centre for Able Pupils at Oxford Brookes University.

She said there was no evidence that summer schools had any long-term impact on children. The Government is funding summer schools this year as part of its plan to encourage children from disadvantaged areas to go to university.

Sir David Winkley, another government adviser and a former primary head, pointed out that primaries faced a particular problem. He said schools were already teaching a crowded curriculum and were up against league tables.

Geraldine Hackett