Ukip hit a record 17% in the ComRes poll for the Independent on Sunday and Sunday Mirror - firmly cementing its third place ahead of the Liberal Democrats.
Asked whether they trusted the duo to make the right decisions about the economy, just 23% agreed - down 6% since last year - while 56% didn't.
Cameron is the only leader who is more popular than his party
Support for the Prime Minister's Tories - pushed into third place by the eurosceptic party at last month's Eastleigh by-election - fell three points to 28%.
Poor poll showings have fuelled calls from activists and MPs for a rightwards shift to counter Nigel Farage's party - a change he has publicly refused.
The poll puts Labour nine points ahead after gaining one point to 37% with the Liberal Democrats - who claimed victory in Eastleigh - also up one on 9%
By a majority of 38% to 28%, those polled said the Tories were more likely to win if they kept Mr Cameron as leader, following a bout of speculation of a challenge.
And he remains the only leader - including Farage - more popular than his own party, by 26% to 23%.
Fewer than one in five (19%) thought Home Secretary Theresa May, the subject of leadership speculation last week, would make a good prime minister.
That was the case among women as much as men, the poll found.
ComRes interviewed 2,015 GB adults online on March 13-14.
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