But Mr Willetts went further in a speech yesterday by claiming that grammar schools widen the gap between rich and poor because middle-class parents exploited the admissions systems.

He told the Confederation of British Industry: “We must break free from the belief that academic selection is any longer the way to transform the life chances of bright poor kids.

“We just have to recognise that there is overwhelming evidence that such academic selection entrenches advantage, it does not spread it.”

As evidence, Mr Willetts pointed to the fact that only two per cent of grammar school pupils receive free school meals. He promised that a future Tory government would instead expand the Government’s city academies by cutting restrictions on parents’ groups, private firms and charities setting them up.

But many Tories fear his comments will be seized on by opponents of selective education to press for the closure of grammar schools.

Sources close to Mr Brady said he had written his outspoken article on the New Statesman website out of concern that the future of grammar schools in his Altrincham and Sale West constituency could be put in jeopardy by Mr Willett’s claims. Other senior Tories savaged the latest Tory policy switch. Former Tory Cabinet minister Lord Tebbit said: “This would be a mistake. Selective education should be available to poor people as well as to rich people who can afford to send their children to exclusive public schools.”

Grammar school-educated Tory MP Roger Gale said: “My party is being extremely foolish if it is going to nail its colours to the city academy mast before we find out whether they will work or not.”

He added: “The concept that only middle-class parents are able to play the system to get their children into grammar schools is bizarre.

“There are still parents from all walks of life who regard the education of their children as of paramount importance and who are prepared to forgo luxuries such as foreign holidays to pay for extra-curricular activities for their sons and daughters. Is that now a crime?”

A survey of 1,000 Tory activists for the Conservative.home website yesterday found more than 70 per cent opposed the party’s opposition to promoting grammar schools. Angry comments swamped the website.

One said: “Another nail in our coffin, and another demonstration of how out of touch David Cameron actually is.”