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A Populus poll for The Times, taken over the weekend, makes Mr Clarke the overwhelming choice among ordinary voters.
But he is not the front-runner among either Tory MPs or party activists, where David Davis, the Shadow Home Secretary, is believed to be ahead.
Two fifths of the public (41 per cent) now think that Mr Clarke would make the best leader for the Tories. This compares with 29 per cent in mid-July. The rise reflects the publicity that he received after announcing that he would stand.
Mr Davis has support of just 10 per cent of all voters, down two points on mid-July. The rest of the candidates are nowhere. David Cameron is largely unknown outside Tory circles and has the backing of 2 per cent of the public, a halving of his support in the past six weeks. Sir Malcolm Rifkind is on 5 per cent, up one point.
The findings were mirrored by an ICM poll for Newsnight on BBC 2 last night which found that 40 per cent of those questioned thought Mr Clarke the best leader, four times as many as Mr Davis.
But neither voters nor Tory supporters will decide the contest. Mr Clarke is much less well placed among either Tory MPs, who will decide under the proposed change in party rules, or party members, who elected Iain Duncan Smith in 2001.
The poll findings came as Mr Davis broke ranks with his leadership colleagues by declaring that it would not be a “bad thing” if party activists rejected new rules for choosing Michael Howard’s successor.
The bookmakers’ favourite to win predicted that local Tory officials would block moves to give MPs, rather than grassroot members, the final say.
His intervention surprised Tory MPs because only this weekend Mr Howard and Francis Maude, the Tory chairman, made speeches to a meeting of senior party officials imploring them to back the changes.
It is widely believed that Mr Davis’s strong position would be boosted if the vote was left to party members. Although Mr Howard’s office declined to comment, senior MPs said that it would be astonishing if he was not angry about Mr Davis’s move. One said: “David is trying to sew this one up. He is putting himself forward as the champion of the activists.”
Mr Clarke said that reports about the state of activist opinion should be taken “with a pinch of salt”. He denied that he would lose out even with a vote of all party members.
His chief aide said that he would be standing whatever the rules of the election. He has e-mailed party members emphasising his desire to take the Conservatives back to power. A friend said: “Ken believes opinion in the constituencies about him has changed. They see him as a winner.”
Mr Howard wants to go soon after the party conference and it had been expected that the contest would be over by mid-November. If the rule change is not accepted it will take several weeks to organise the ballot of members to choose the new leader and that could mean it will be delayed until January.
Mr Davis said on the Today programme on BBC Radio 4 that it would have been better if the activists had been allowed to come up with a shortlist of two names and for MPs to make the choice from those names. He said: “I think the new proposal to do away with the rights of the membership is likely to be turned down. I don’t think that’s a bad thing.
“I think it would have been much easier just to say to the party in the country, ‘Why don’t we reverse the order — you have the first hit and MPs have the last say?’ That way, we could have avoided the issue of having somebody elected without majority support in the House of Commons.” The issue was to be “revisited” after the forthcoming election, he predicted.
Senior MPs said that Mr Davis’s proposal risked opening the party to ridicule.
One said: “Imagine the furore if the party voted for two names and neither of them were Ken Clarke, easily the public’s favourite Tory. Some people are clearly getting nervous about Ken’s strong start.”
Andrew Tyrie, a member of the Clarke campaign, said that the polls showed that even before he became leader Mr Clarke could generate enough additional support to win an election for the Conservatives.
Another supporter said: “These polls will be noticed by the wider party, which is why Ken can win even if in the end it is a vote by the whole membership.”
Populus interviewed a random sample of 1,506 adults by phone between September 2-4.
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