Twenty per cent of the public said they would be more likely to vote Conservative if he led the party, putting him leagues ahead of his Tory rivals in terms of public popularity.
The poll confirms claims by allies of Mr Clarke that he is the Tory contender most likely to win over Labour and Liberal Democrat voters after years of stagnation in the polls.
The results of the first public opinion poll on the leadership race will bolster Mr Clarke's argument that he is the Tory MP most likely to lead the party to victory at the next election.
Forty per cent polled said they thought Mr Clarke would be the best Tory leader, compared to 10 per cent for David Davis, who is seen as the front-runner. The ICM poll for BBC's Newsnight also found that only 4 per cent of the population felt that fellow candidates David Cameron and Sir Malcolm Rifkind would make the best leader. Three per cent favoured Liam Fox, and 2 per cent David Willetts.
While 20 per cent said they would be more likely to vote Tory with the former chancellor leading the party, only 8 per cent said they would be less likely to vote Tory if he got the top job. The poll found that 7 per cent would be more likely to vote Conservative if Mr Davis were leader, but 10 per cent said his leadership would be a turn-off.
Today Sir Malcolm will begin a 12-day tour of marginal constituencies in a bid to give impetus to his campaign.