The survey found that among Lib Dems, 50.1 per cent want Mr Cameron as Prime Minister and 30.3 per cent want Gordon Brown. Only 19.6 per cent choose their party leader Sir Menzies.
The survey has been carried out by Conservative MP Philip Dunne among voters in his Ludlow constituency.
Mr Dunne wrote to over 38,000 voters and received 6,400 replies - an extraordinary public response to such a poll.
Based on a sample of 3,350 replies, Mr Cameron emerged as the clear choice across the constituency as the best Prime Minister for Britain. He scored 80 per cent, winning the backing of 50 per cent of Lib Dem Supporters, 32 per cent of Labour supporters and 94 per cent of Conservative supporters.
Mr Brown was backed by only 13 per cent of all voters and 62 per cent of Labour supporters. One in three Labour voters wants Mr Cameron as Prime Minister. Sir Menzies had the support of only 7 per cent of all voters and under 20 per cent of Lib Dems.
The poll also reveals that Tony Blair has outstayed his welcome as Prime Minister.
Of those who voted Labour in 2005, 73 per cent believe Mr Blair should step down before the May elections.
Overall, 65 per cent of people want Mr Blair to step down before Christmas. A startling 85 per cent of all voters want him gone by the May elections.
Labour voters back Gordon Brown (51 per cent) ahead of John Reid (27 per cent), well ahead of other potential contenders, such as Alan Johnston (5 per cent), who is on the same level as David Miliband, only just ahead of John Prescott.
Just over a year ago, Mr Dunne polled 45,000 local voters on the Conservative leadership race. Based on replies from 6,725 residents, among Conservative supporters Mr Cameron (56 per cent) had a clear lead over Kenneth Clarke (28 per cent) with David Davis a distant third (10 per cent).
Mr Cameron went on to win the vote among Conservative Party members by a margin of 2:1 over Mr Davis.
Mr Dunne said: "These are fascinating results. They show a collapse in confidence in Sir Menzies Campbell among Lib Dem supporters. It is quite extraordinary that local Lib Dems would rather have David Cameron as Prime Minister and that one in three Labour supporters favour Mr Cameron as well.
"This is a grave blow to the Lib Dems and suggests that they miscalculated badly when they got rid of Charles Kennedy. But it also shows that David Cameron's moves to modernize and change the Conservative Party are striking a real chord with voters."
