The Greens have decided to devote only limited resources to next month’s Makerfield byelection, the Guardian has learned, in a potentially significant boost to Andy Burnham’s chances of winning the seat.

The party is instead expected to focus more on the byelection for the Greater Manchester mayoralty, which will be triggered if Burnham is returned to parliament, senior Green figures have said.

The party is fighting the Makerfield seat, having announced Sarah Wakefield as its replacement candidate for the 18 June contest, after the initial choice, Chris Kennedy stood down following revelations about social media posts.

This would involve “taking the fight to Reform and asking which version of Andy Burnham is going to show up”, with a focus on the Labour candidate’s positions on areas including electoral reform and the public ownership of utilities, one senior Green said.

But following a lively debate within the party, there will not be a repeat of the mass mobilisation of activists seen in February’s Gorton and Denton byelection, where the party overcame a 13,000-plus Labour majority to win the seat.

While Makerfield is also in Greater Manchester, it is some distance from Gorton and Denton and demographically very different, and thus seen as a much greater challenge for the Greens to win.

A number of senior party figures, including Caroline Lucas, the Greens’ first MP, and Jonathan Bartley, who co-led them with Lucas, have called for Zack Polanski, the leader of the party in England and Wales, to scale back any campaign, particularly if Burnham will commit to electoral reform.

In a letter with other Green figures over the weekend, Bartley said that given it was a seat the party was unlikely to win, and a split vote on the left could help Reform UK take the constituency, should Burnham commit to proportional representation then “on this unique occasion, we don’t think Greens should run a full campaign against him.”

Such views have prompted anger among some others in the party, particularly leftwing members who have joined since Polanski took over the leadership last year, overseeing a near quadrupling of membership. They argued that the Greens want to replace Labour, and so should try to defeat Burnham.

While the campaign is being run by the local party, which has significant independence, a full-blown effort would need both the support and resources of the central party under Polanski, and it is understood that the decision has been made to not do this.

“I doubt we are going to be bussing people in to Makerfield to door-knock,” one party source said.

Another senior party figure said the team around Polanski had come to the realisation that there was more harm to be potentially done than benefits to gain: “They know they can’t win, and it would be terrible to be blamed for letting Reform in.”

In another potential boost to Burnham’s chances, a constituency poll in Makerfield indicated a possible split on the right, with Restore Britain, the far-right organisation formed by ex-Reform MP Rupert Lowe, shown as coming third on 7%, behind Labour and Reform, albeit on a sample size of 369 voters, once those who were undecided were removed.

On Tuesday, the Greens announced that Sarah Wakefield, who was elected earlier this month to Manchester city council, would stand for the party. The 38-year-old is a charity director who is currently on maternity leave.

It came after the original candidate, Chris Kennedy, was announced last Tuesday but dropped out just nine hours later, the party citing “personal and family reasons”.

The Times reported it had approached Kennedy about a series of social media posts he had shared about an attack on Jewish ambulances in north London in April. An Instagram video shared by Kennedy described the arrests of two men over the incident as “total bullshit to keep the false flag flying”, the paper reported.