Jess Phillips has said Sir Keir Starmer will still likely be ousted from No 10 even if Andy Burnham is not able to return to parliament to challenge him.
The prime minister has faced immense pressure on his position in recent weeks, following disastrous results in the local elections earlier this month.
Almost 100 of his own MPs called for his resignation, while multiple ministers – including Ms Phillips and former health secretary Wes Streeting – resigned.
A leadership challenge has yet to be officially triggered, with other challengers appearing to be waiting for the potential return of the mayor of Greater Manchester to Parliament.
But, despite Mr Burnham being widely seen as Sir Keir’s most likely successor, Ms Phillips has said a challenge will go ahead regardless of his success in the Makerfield by-election.
“I think even if Andy Burnham doesn’t win in Makerfield there will be a change of the prime minister,” she told Hay Festival.
“I’ve never been to Wigan in my life, so I have absolutely no idea about the people there, so I shall go and find out. But, yes, I imagine Andy Burnham will win it, and I imagine then that the prime minister changes.”
Ms Phillips stepped down from as safeguarding minister earlier this month, joining a string of mostly junior ministers quitting in protest at Sir Keir’s leadership.
She accused him in her letter of failing to act fast enough on violence against women and girls, saying his “desire not to have an argument means we rarely make an argument, leaving opportunities for progress stalled and delayed”.
Speaking at the festival, Ms Phillips said she felt “liberated” since resigning as safeguarding minister with a scathing letter accusing the prime minister of failing to be “bold”.
She said on Monday: “I can sort of see where Keir Starmer and Keir Starmer’s loyalists come from, in that the idea that we could repair a country so badly broken after years of austerity quite so quickly, is just a lie.
“But then also what he has not done is grab that particular mantle or even actually tell the story.”
The prime minister has vowed to stay on as Labour leader and insisted he will fight any official challenge that is launched against him.
But the fallout of the disastrous local election results has exposed deep splits within the Labour Party, throwing Sir Keir’s government into chaos.
Splits within the cabinet have been on full display, after the health secretary, Wes Streeting, dramatically resigned following days of intense speculation.
The MP and former health secretary told reporters on Friday that he held off triggering a leadership race to give Mr Burnham time to tread a path back into the Commons.
If Mr Burnham wins the Makerfield by-election, he will likely use his return to parliament as an opportunity to trigger a leadership contest against Sir Keir, which polls suggest he would win.
But allies of Mr Burnham have suggested he may not launch a bid for the party leadership immediately if he is successful in the June 18 contest.
