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The former deputy prime minister, whose past interventions over the Tory leadership have been influential, last week met David Cameron, the centre-left leadership challenger.
The talks at the peer’s London home were held at the request of Cameron, the shadow education secretary. He wanted to gauge whether Heseltine, one of the key figures on the centre left of the party, would back him.
Their discussions came amid speculation that Clarke is about to announce that he will stand for the leadership after months of openly flirting with the idea.
If the former chancellor, a pro-European who is also considered to be a left-wing Tory, were to stand he could take crucial votes from Cameron when MPs make the final decision in November.
But Heseltine is understood to have told Cameron, who is running second in the bookmakers’ stakes to Davis, that he is still a firm supporter of Clarke.
Tory insiders say Heseltine believes that a dream ticket, with Cameron running as Clarke’s deputy, could be a formidable alliance that could derail Davis’s campaign.
Last week Cameron refused to rule out doing a deal with Clarke if there was a lack of support for him to win outright. In June Clarke and Cameron met for private discussions but failed to reach a deal on the leadership.
Heseltine also believes that Cameron, still only 38, could gain valuable experience running as Clarke’s No 2.
“It is not like Gordon Brown waiting years for Tony Blair to give up the top job; Ken is 65 so he is not going to be hanging around for much longer,” said an ally of the Tory peer.
Several MPs believe that Davis has only about 60 MPs out of 196 firmly backing him — not enough to guarantee victory.
In addition many of the new intake of 51 Tory MPs are undecided and could hold the key to the leadership election.
A source close to Heseltine said: “Michael said he would stay with Ken. He still thinks it all could have been very different at the general election if Ken had been elected party leader in 2001.
“But he believes there should be a beauty parade of candidates at the party conference. He is not sure that David Davis has got much more than 40% of the votes in the parliamentary party so it is all up for grabs.
“Michael believes that if Cameron is not sure he can win outright on his own then the dream ticket of him and Ken could be enough.”
Heseltine enjoys a reputation as the Tories’ kingmaker. He is deemed by some MPs as responsible for bringing about the downfall of Margaret Thatcher and also made critical remarks about Iain Duncan Smith that added to the pressure on the Tory leader who was ousted in 2003.
Cameron’s camp yesterday played down the significance of the discussions with Heseltine, saying that he had merely requested the meeting as part of a consultation process with the party’s grandees.
They said that Cameron had also sought the advice of Sir John Major, the former prime minister.
A source close to the shadow education secretary said: “When you are running for the leadership of the party it makes sense to listen to senior people in the party. David merely asked to see Heseltine for some advice.”
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