Mr Cameron has kept silent about rumours buzzing around Whitehall. He and his campaign team argue that answering one question about his personal life will simply invite more.
Last night he once again refused to answer the question of whether he had taken drugs, saying that politicians should be allowed to "err and stray " before they enter public life.
David Dimbleby asked him whether he had ever taken Class A drugs. Speaking on Question Time, Mr Cameron replied: "I have not answered the question about drugs because I think that is all in the past and I don't think you have to answer it. We're both allowed to have had a private life before politics in which we make mistakes and we do things that we should not and we are all human and we err and stray."
But Liam Fox, one of the outsiders in the leadership contest, confirmed to journalists that he had never taken class A drugs. The former GP said: " I've seen too many people suffering from the effects of drugs brought into A&E."
His assertion followed a comment by another leadership candidate, Kenneth Clarke, who said he had never taken cocaine.
Edward Leigh, a senior backbencher, urged Mr Cameron to answer the same question. "I think it does matter. He should tell the truth," Mr Leigh said. Despite the questions over his past, Mr Cameron's position in the leadership race was looking stronger than ever after two MPs who voted for Mr Clarke in previous contests, Jacqui Lait and Robert Key, came out for him. He now has the public backing of 34 MPs. Mr Cameron had a private meeting yesterday with the media mogul Rupert Murdoch.
The front-runner, David Davis, whose campaign appeared to have hit the rocks after a disappointing performance at the annual conference, gained the support of one of the new MPs, James Brokenshire, to bring his total to 66. Mr Clarke and Mr Fox are now in a close race to avoid being eliminated in the first ballot on Tuesday. When nominations closed at noon yesterday, no other MPs had decided to join the race.
Mr Clarke was boosted by a letter from 50 leaders of Tory groups on borough and district councils. It said he was "the only candidate with the combination of experience, energy and popular appeal that we need". His team also released a letter of support from eight Tory peers.
But Mr Clarke came under attack over his role as a non-executive deputy chairman of British American Tobacco. Writing in the British Medical Journal, Mike Daube, professor of health policy at a university in Perth, Australia, said: "If he is elected, companies such as BAT will flourish with access at the highest levels, while their products kill more and more millions."
Dr Fox closed the gap on Mr Clarke by announcing the names of four previously uncommitted MPs who vowed to vote for him. This brought his total of known supporters to 20, compared to 23 for Mr Clarke. So far, 143 out of 197 MPs have said who they are supporting.