Sir Keir Starmer could face leadership threats from Andy Burnham and Yvette Cooper

Sir Keir Starmer could face a threat to his leadership from two former frontbenchers after both Andy Burnham and Yvette Cooper signalled they still have designs on Labour’s top job.

Ms Cooper, who is the chairman of Parliament’s home affairs committee, did not rule out running in any future race while Mr Burnham, who is now the mayor of Greater Manchester, said he would fight for the leadership if he had the support of Labour colleagues.

Both served as Cabinet ministers under Gordon Brown before running for the leadership in 2015 and losing to Jeremy Corbyn.

On Sunday, Mr Burnham said he would run after the next election and suggested Labour would have lost fewer Northern seats at the 2019 election under his stewardship.

"I still think life would have been different if I had won," he told the Observer.

Mr Burnham romped to re-election in the Manchester mayoral race on May 6, taking all 215 wards in Greater Manchester.

"I think we would be stronger in taking on the Government,” he added.

His comments came as Ms Cooper, the former Labour work and pensions secretary, refused to rule out running for the leadership again.

Ms Cooper had been tipped for promotion in the recent Labour reshuffle, but remains on the back benches.

She said she had not been approached by Sir Keir’s office to serve in the party’s top team.

“It's for Keir to decide who he wants in his shadow cabinet and what kind of shadow cabinet he wants,” she told the BBC’s Andrew Marr Show.

Asked directly if she would run in a Labour leadership election, Ms Cooper replied: “I think we've got a leader of the Labour Party.

“He's getting on with the job, and actually this is a challenge for the whole of the Labour Party to show we're a party not just of the cities, but of the whole country.”

The suggestion that two former Labour Cabinet ministers are considering standing again comes amid mounting pressure on Sir Keir to demonstrate that he can unite the party and win back Red Wall seats lost at the last election.

A new policy review, designed to formulate manifesto policies, will be chaired by Anneliese Dodds, who until recently was Labour’s shadow chancellor of the exchequer.

Ms Dodds lost her position to Rachel Reeves, the former shadow chancellor of the Duchy of Lancaster, who in turn was replaced by Angela Rayner in a three-way reshuffle.

The rising influence of Ms Reeves, Ms Cooper and Mr Burnham will worry the party’s Left-leaning backbenchers, who have complained Sir Keir’s top team is increasingly skewed towards Right-wing, “Blue Labour” voices.

Members of the Socialist Campaign Group, a Leftist caucus on the Labour benches, complained that Ms Rayner’s sacking from her previous role as party chairman was a sign Sir Keir was “scapegoating” the Left for Labour’s election woes.

Any challenge to Sir Keir is unlikely to happen soon, with potential runners in a leadership election happy to let him manage the difficult job of rehabilitating his party’s image with the electorate.

Mr Burnham said he would not be challenging Sir Keir for the leadership before the next election or "any time soon", but added: "If there comes a point where it is clear to me that the Labour Party, having not thought me right twice, suddenly thinks 'well actually you probably are now, because of the way the world has changed', then as I say, I will put myself forward to lead the Labour Party."

Bookmakers on Sunday slashed his odds to become the next leader.

Ladbrokes put Mr Burnham at 4/1, ahead of Ms Rayner at 5/1.