Andy Burnham faces a perilous race to win the Makerfield seat, his allies have said, as he gears up to fight a byelection that could decide the long-term future of Labour and the country.

The Greater Manchester mayor is likely to be confirmed as Labour’s candidate for the north-west constituency later this week, but those close to him say he faces an uphill battle to beat Reform UK. Nigel Farage’s party won more than 50% of the vote at the local elections and polling suggests Burnham is only marginally ahead.

Reform is likely to focus heavily on immigration and Brexit over the next few weeks as it looks to exploit an escalating Labour row over whether the UK should seek to rejoin the EU.

The outcome of the byelection is likely to determine not only the immediate political future of Keir Starmer, whom Burnham has pledged to challenge if elected, but also the viability of the Labour party as a whole.

The prime minister spent the weekend at Chequers considering his political future, and allies say that despite his public defiance he is now willing to stand aside should Burnham win a clear mandate in Makerfield and no other challenger emerges.

If he loses the byelection, it will leave Starmer in office but badly wounded by weeks of damaging attacks from his own MPs and without an obvious successor. One ally said: “It’s impossible to underscore how perilous this is. I would give Andy a 45% chance of winning, maybe a bit more than that.

“It’s compelling to say tell progressive voters to vote for Andy to get Starmer out, but the flip side is you’re saying to Reform voters that if they vote Reform they can finish the Labour party off for good.”

Burnham spent the weekend in Greater Manchester, campaigning in Makerfield and in talks with senior Labour figures involved in the selection process. Applications to run in the seat close at midday on Monday, with a formal candidate recommendation from Labour’s ruling executive committee on Thursday. If Burnham is the only applicant, the process might happen more quickly.

A vote in the seat is likely to be held on or around 18 June, giving Labour and Reform a four-week sprint before what could prove to be one of the most consequential byelections in British political history.

Pollsters say that despite the local election result, Burnham’s personal popularity across Greater Manchester gives him an even shot of winning the race.

Luke Tryl, the director of the research group More in Common, said: “We have two amazing forces playing against each other – the demographics of the seat, which all point to a Reform win, versus Burnham’s personal factor.

“It makes the result really consequential. If Labour can’t win they may as well pack up and go home. If they do win, all bets are off in terms of the prime minister’s future.”

Labour figures say they believe Burnham’s job was made harder over the weekend by a public row about whether the UK should rejoin the EU after comments from another likely leadership rival, Wes Streeting.

Streeting said on Saturday that he believed Britain’s long-term future lay in rejoining the union – something that was quickly dismissed as “odd” by the culture secretary, Lisa Nandy.

Reform is hoping to focus heavily on Labour’s position on European membership during the campaign, putting Burnham in a difficult position of deciding whether to side more closely with the wider Labour membership, which is overwhelmingly pro-EU, or voters in Makerfield, 65% of whom voted to leave in 2016.

Labour’s position will be further tested on Wednesday when the Liberal Democrats lay an amendment to the king’s speech calling for the government to begin immediate talks over entering a customs union.

Starmer has ruled out such an agreement, but colleagues including Streeting argue this has hampered the government’s attempts to boost growth.

Immigration is also likely to feature heavily in the byelection campaign, putting Burnham in an even more difficult position. Many Labour members, whose votes he will need in a leadership contest, are pushing for the government to water down its changes to the asylum system, while many voters in seats such as Makerfield are calling for an even harder line.

Tom Baldwin, a former Labour official and Starmer’s biographer, said: “If Burnham says things which put him in opposition to a much closer relationship with Europe, or appears to adopt a hard line on immigration in order to win the byelection, it might yet make it harder for him to win the next election – among the party membership which appears to take a much more progressive view on these issues.”

Streeting will reiterate his pro-EU stance this week when he gives a closely watched resignation speech in the Commons.

Allies say he intends to argue that the government has not been bold enough in its policies or its political arguments, and wants to focus not only on the EU relationship but also wealth taxes and the role of technology in people’s lives.

“There is no point in trying not to upset anybody, that’s what got us into this problem,” one said. “Sometimes you have to be willing to upset people to get things done.”

While his potential successors jostle for position, Starmer is said to be reconsidering his previous determination to fight a leadership contest in any circumstances.

Downing Street insisted on Sunday that he would stand again for the leadership if challenged, but friends say his position is softening.

After a weekend at his official country estate, he is understood to have decided to delay a decision about his future until after the byelection, when it will become clearer whether he will have to face a challenge and from whom.

One friend said: “His position is not ‘I will stand, come what may’. It depends on what happens, but at the same time it’s about not rushing to positions that might suit particular other factions in the Labour party.”