David Cameron on Sunday night looked as though he had weathered the recent storm over drug use that has engulfed his campaign for the Conservative leadership after his main rival said he had “absolutely got the right” not to answer questions about the issue.

As Conservative MPs prepare to decide this week which two men will battle over the leadership in a nationwide poll of party activists, David Davis, one of the leadership front-runners, said the row over Mr Cameron and drugs would quickly “fade out”.

Mr Cameron, the 39-year-old former Etonian, has refused to state explicitly whether he has used narcotics, including Class A drugs in the past.

Speculation over the issue looked last week as though it could derail his strong chances of winning the leadership in a contest that will be concluded in the first week of December.

But Mr Davis's comments on Sunday came on the back of a string of developments which reinforced Mr Cameron's stance on the drugs issue including an opinion poll which showed that some 61 per cent of Tory supporters believe there would be no reason for a candidate to stand down, even if he confessed to using hard drugs.

Mr Cameron continues to be the candidate with the most momentum as the contest for the Tory leadership formally gets under way this week.

In two secret ballots the first on Tuesday and the second on Thursday MPs are to decide which two men should go forward to contest the leadership in a national vote involving the Tories' 300,000 activists.

Mr Cameron and Mr Davis are seen by most Tory MPs as the two most likely to be selected. Kenneth Clarke, who has acknowledged that he is relatively weak in terms of support among new Tory MPs, could well be eliminated in the first ballot.

When the result of the first ballot is announced, on Tuesday night, the spotlight will be on Mr Davis. At the Conservative party conference earlier this month, the shadow home secretary appeared to be the clear leadership front-runner, backed publicly by 65 MPs.

Mr Davis needs to emerge on Tuesday night with more than 65 votes to give himself momentum into Thursday's final ballot.

If he gets at least 70 votes, Mr Davis will be able to argue that MPs have shrugged off criticism of his lacklustre style, and that he is the clear standard bearer of the Tory right.

But if Mr Davis gets fewer than 65 votes, his detractors will argue that his campaign has stalled and that his supporters have taken fright.