Jeremy Corbyn should recognise he cannot return Labour to power and quit for the good of the party, a pro-Brexit MP said.
Frank Field praised Mr Corbyn for focusing on public frustrations with the impact of globalisation but said his pitch was tainted by "serious claptrap" in other areas.
The embattled Opposition leader has rejected calls for his resignation amid growing fury at his failure to galvanise the party's traditional supporters to turn out in favour of EU membership.
There is alarm within the party at the way a series of traditional Labour strongholds in the North and Midlands voted heavily for Leave, with many voters citing concerns about immigration.
Mr Corbyn is facing a vote of no confidence from some of his MPs, as many express concern at the possibility of him leading the party into a snap autumn general election.
He insisted he will be carrying on and "making the case for unity" - beginning with a speech on immigration and the consequences of Brexit later today.
But Frank Field said he should use the speech to follow Mr Cameron and announce his departure.
"One of the dilemmas that we have is that Jeremy is the only senior politician who has tried to grapple with and put forward views of that group of the electorate who are the losers by globalisation," he told BBC Radio 4's Today.
"Jeremy's problems are that he packages this with serious claptrap. For example our defence policy that we will have Trident, we will renew Trident but of course we won't have any weapons, has our supporters and probably the rest of the country lying down on the floor and yelling with rage or just simply crying
"We are into an era of new politics where those people who have lost out clearly by globalisation, for the first time have found their voice through the referendum to saying in this country 'enough is enough'.
"What Jeremy has been trying to do, with his social justice programme, is begin to answer those questions that are posed by the losers of globalisation but he clearly isn't the right person to actually lead the party into an election because nobody thinks he will actually win.
"I would very much like him to do that and set the debate going with that kind of flavour."
He sounded a note of caution about the chances of ousting Mr Corbyn, noting that the membership - including many who signed up on the back of the leader's campaign - remained "very clearly in favour of somebody like Jeremy".
And he said he was unable to identify the best replacement, adding that "we don't want the same old claptrap from the Blairites either".
Labour MPs are fearful the resignation of Mr Cameron as Prime Minister could trigger a general election before the end of the year, with critics of Mr Corbyn warning they needed to act to prevent a catastrophe at the polls.
Dame Margaret Hodge has submitted a no confidence motion to Parliamentary Labour Party (PLP) chairman John Cryer with a request that it should be discussed at the next meeting of the group on Monday, with a vote the following day.
Asked if he will resign, Mr Corbyn told Channel 4 News: "No, I'm carrying on.
"I'm making the case for unity, I'm making the case of what Labour can offer to Britain, of decent housing for people, of good secure jobs for people, of trade with Europe and of course with other parts of the world. Because if we don't get the trade issue right we've got a real problem in this country."
Dame Margaret emphasised that under PLP rules it would be a secret ballot for her motion, in the hope that MPs will be emboldened to move against Mr Corbyn without the fear of a backlash from his grassroots supporters from the Momentum campaign group.
Although the motion has no formal status, backers hope it will help build a sense that confidence in him is draining away, forcing him to resign.