Conservative leadership contender Ken Clarke is four times more popular with ordinary voters than his nearest rival, a BBC Newsnight poll suggests.
Ken Clarke says he is the most popular candidate
Of those questioned, 40% said Mr Clarke would make the best leader, compared with 10% for David Davis and 4% for David Cameron and Malcolm Rifkind.
The poll suggests 20% of people would be more likely to vote Tory with Mr Clarke as leader, and 8% less likely.
ICM interviewed 1,007 adults at random by telephone between 2 and 4 September.
David Davis could lose the party more votes than he could gain, the poll suggests.
Seven per cent of those questioned by ICM Research said they would be more likely to vote for a Davis-led Conservative Party - but 10% would be less likely.
Welcoming the poll, Mr Clarke said: "It is nice to know that such a wide section of the public hold me in such high regard and have confidence in me.
"The poll shows that under my leadership, the Conservative Party would have the prospect of winning the next election."
But supporters of Mr Cameron, the youngest of the candidates, say Mr Clarke's strong showing was down to "recognition factor".
Andrew Robothan MP told BBC Two's Newsnight: "I think it would be surprising if the Conservative Party would go into a general election in 2009 with somebody who was first a minister for Edward Heath in 1972 - 37 years before.
"We need to appeal to younger people who have not voted Conservative, not people of my age, 54, who already vote predominantly Conservative."
Stephen Dorrell MP said it was "an extraordinary tribute" that Mr Clarke could still "connect directly with people other Conservatives have failed to connect with".
There is speculation an attempt to give MPs the final say in the choice of new leader may be rejected later this month.
The election would then take place under the current rules, which give all Tory members a vote.
That could delay the election result until later in January. Grass roots members voted for Iain Duncan Smith over Mr Clarke in 2001 - although the former chancellor says he can win their support this time.
Interviews were conducted across the country and the results have been weighted to the profile of all adults.
Liam Fox was the favourite of only 3% of those questioned and David Willetts of only 2%.
And 4% of people said they thought none of the six named candidates would be best, with another 33% undecided.
Mr Clarke's support appears weakest in the 18-24 age group - where 23% said they thought he would make the best leader. But he was favourite among half of those aged above 55.
Mr Cameron had his best showing (8%) in this age group.
Only Mr Clarke and Sir Malcolm Rifkind have publicly declared they will contest the leadership, although Dr Fox is expected join the race later this week.
Sir Malcolm will try to boost his campaign on Tuesday when he begins a tour of Britain in Derbyshire.
He says there must be no "no go areas" for the party and is visiting activists in marginal constituencies and areas where there are few or no Tory MPs.
The former foreign secretary said: "Consultation between MPs and party activists is vitally important all year round. Activists are the lifeblood of our party...
"Our plans for rebuilding the party must be focused on how we can win back support in those areas of Britain where Conservative support has declined."