The Provost of Eton College has threatened to resign from the Conservative Party over Government plans to make employers ask candidates whether they attended an independent school.

Lord Waldegrave of North Hill, a former Tory Cabinet minister, has told Conservative officials he cannot accept proposals published last week.

He issued the warning after Matt Hancock, the Cabinet Office minister, said companies should ask job applicants whether they went to private school in an attempt to stop discrimination against the poor.

His comments puts David Cameron at odds with the most senior individual at the school he used to attend.

Lord Waldegrave, who served in the governments of both Margaret Thatcher and John Major, said he believes the Prime Minister's policy would discriminate against children at fee-paying schools.