The move by Damian Green, a former shadow cabinet member, and Ian Taylor, a leading ally of Ken Clarke, suggests the right-wing MP is succeeding in attracting support from unexpected quarters of the party.

Davis has yet to declare he will run for the leadership when Michael Howard steps down later this year, even though most of the other potential candidates have done so.

Green, whom many would have expected to support either Clarke or David Cameron, the 38-year-old shadow education secretary, grew to admire Davis when they worked together on Tory plans to boost “localism” — giving more power to patients and parents — before the general election.

“I have come to the conclusion that the Conservative best placed to offer a new Tory idealism is David Davis,” writes Green in an article (see below) for The Sunday Times.

Meanwhile Taylor, who is close to Clarke and backed him for the leadership in 1997 and 2001, said: “David Davis could be the man for me. David has a strong base within the party on the right wing and that is the more dominant part of the party.

“Having been one of Ken’s supporters in 1997 and 2001, I am trying to see if we could form some kind of coalition across the party, reaching out to the vast section of the population that seems to want to ignore us.”

Other Clarke allies are urging him to stand, however, including David Curry. “The next Conservative leader will have to face prime minister Brown and perhaps in a situation where the economic situation is less comfortable for the government than it has been,” said the Skipton and Ripon MP.

“You have to ask, who would be the best person to take on Brown in a real political maul and score points. As far as I’m concerned there is only one man and that’s Ken.”

Clarke, the Europhile former chancellor, remains popular with some sections of the party and is likely to declare his candidacy this weekend, potentially causing a fight between him and Cameron for the votes of centre-left Tory MPs.

Tension is building as members of the Davis camp jostle for the initiative with likely rivals. The Davis and Cameron factions are already counterclaiming that each is briefing against the other.

Cameron is supported by MPs including Tim Yeo, the former environment spokesman, and Boris Johnson, editor of The Spectator magazine and the member for Henley. Oliver Letwin, the former shadow chancellor, is also said to be a backer. “He is a very strong candidate,” Johnson said. “I think I will support him.”

Yeo, another centre-left Tory, signalled he was pulling out of the leadership race this weekend. “Each of us needs to make an honest appraisal of our prospects,” he said on GMTV.

He said more of the eight candidates should step aside to make way for a clear challenger. “I hope we can use the summer recess to find someone to group around.”

Davis remains the bookies’ favourite to win and a straw poll of Tory backbenchers conducted by The Sunday Times this weekend suggests he is ahead among MPs.

Last week Tory MPs rejected Howard’s plans to change the leadership election rules and voted to restore the power to appoint his successor to the parliamentary party. William Hague, the former party leader, changed the rules in 1999 and gave the grassroots membership the final say.

Candidates for the leadership are likely to go before “hustings” at the Tory conference this autumn ahead of the contest. Other contenders include Sir Malcolm Rifkind, the former foreign secretary, Liam Fox, shadow foreign secretary, Alan Duncan, shadow transport secretary, and David Willetts, shadow trade secretary.

In the straw poll of MPs Davis came out top. Out of 197 Tory MPs, only 51 responded and of those only a minority would say who they backed. However, Davis was the most popular among these, backed by nine MPs. Four favoured Fox, with three backing Cameron and two Willetts.

The Sunday Times poll showed that while most MPs wanted Howard to step down in his own time, 11 out of 51 thought he should go sooner, possibly before the summer recess next month.

The majority also said they favoured lower taxes, rather than moving further towards the Labour position of increasing public spending.

One MP who participated in the survey said: “The sooner the leadership matter is decided, the better for the party. The Conservative party is a party of the people. We are the low tax party and now the EU constitution is dead, we should scale it back giving countries more individual powers.”

Explore UK News

• Crime News

• Education News

• Health News

• Science News

• Scotland News

Times Recommends

• DIY video helps the WI get to grips with sex
• Artists urge nation to save Titians
• Go home, Iraqi leader tells Britain