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Among both Conservatives and the wider public, Clarke is the most popular candidate to head the party. Despite this, the poll finds that if Brown were to be prime minister, the Labour lead would be even wider than it is now.
Currently Labour has 37% support in the opinion polls with the Tories on 32%. If Clarke led the Conservatives and Brown led Labour, the margin would be 42% to 31%.
The findings suggest none of the potential Conservative leaders offers their party any kind of political lifeline. They will add to a growing sense of pessimism among many party members that none of the available candidates will give them a realistic chance of winning the next election.
Anthony Steen, a Tory MP since 1974, last week described the party as being “in the wilderness without a Moses”.
The YouGov poll of more than 1,800 voters, conducted last Thursday and Friday, shows that Clarke is overwhelmingly the most popular of the leadership contenders, gaining nearly three times the support of Davis.
Excluding “don’t knows”, Clarke achieved 42% support, compared with 16% for Davis, 9% for Liam Fox — who declared his candidature last week — and 6% each for Sir Malcolm Rifkind and David Cameron.
Among Tory supporters, Clarke still had a decisive lead, with 42% support. Davis, however, increased his share to 28%. Fox had 13%, Cameron 8% and Rifkind 4%.
There is evidence in the poll that, among Tory supporters at least, Davis is losing support to minor candidates, some of whom have yet to declare formally.
Asked whom they would back in a straight fight between Clarke and Davis, they divided equally.
The election of a new Tory leader in the party’s third such contest since 2001 will do little for the Conservatives’ overall support, the poll suggests. Labour’s replacing of Tony Blair with Brown, by contrast, would give the government a big political boost, gaining support mainly from Liberal Democrat voters.
The position would be even worse with Davis as leader and opposing Brown than it would be with Clarke in charge. On this basis, Labour would be on 44% and the Tories 30%, enough to give Brown a landslide victory bigger than Blair’s in 1997 and 2001.
The poll comes as Davis plans to bring forward the formal announcement of his candidacy to counter the head start built up by Clarke.
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