Andy Burnham’s decision to appear at a progressive rally alongside prominent Green and Liberal Democrat figures has sparked anger among some Labour MPs, who have accused him of undermining their local election message.

The Greater Manchester mayor, who is seen as one of the most likely challengers to Keir Starmer for the Labour leadership, will be speaking at the Change:Now event this month organised by the leftwing group Compass.

Compass’s founder, Neal Lawson, has long campaigned for a cross-party progressive alliance but is also a prominent supporter of Burnham.

Two other Labour MPs, Clive Lewis, who has offered to give up his seat for Burnham, and Miatta Fahnbulleh, the communities minister, are also due to speak at the event. Other speakers include Caroline Lucas, the former Green party leader; James Meadway, the head of the Green-aligned thinktank Verdant; Vince Cable, the former Liberal Democrat cabinet minister; and the Lib Dem MP Roz Savage.

The event is designed to show how progressives can work across party barriers, something Burnham has long advocated. But its timing, weeks after local elections that are pitting Labour against the Greens in many places, has infuriated many of his colleagues.

Luke Akehurst, the MP for North Durham and a supporter of Starmer, said fellow Labour members should not be speaking at an event with Green politicians and campaigners given the recent antisemitism controversies their party had faced. Two Green candidates in London were recently arrested for alleged antisemitic social media posts, while the party is investigating others over what they have posted online.

“Anyone in the Labour party who has been advancing the concept of a progressive alliance involving the Greens should surely be reconsidering this at the moment given the revelations about the extent of antisemitism amongst their council candidates,” Akehurst said.

Another Labour MP said: “Activists and candidates around the country are fighting for Labour seats on councils; now is not the time to talk about coalitions. It was bad enough when Andy said he’d work with [Jeremy] Corbyn (and Your party); now he wants to work with another party riddled with antisemitism? It’s unconscionable.”

Burnham did not comment. An ally said: “It’s ridiculous to suggest Andy is supporting other parties. He is advancing progressive ideas to help the Labour party. Do people not want anyone sharing ideas or having a debate about where progressives should go?”

Lawson defended the event, arguing that it represented a crucial route to progressive success. “In a multi-party reality, facing huge complex issues, progressives are going to have to work together on ideas to defeat Reform and the causes of Reform,” he said. “When the old politics of factionalism and hyper-tribalism are turning the public off politics, we need the space to think through the policies that will change the country for the better.”

Fahnbulleh and Lewis have been contacted for comment.

The event, which takes place on 30 May in east London, will gather thinktanks, politicians and academics for “a day of debate, disagreement and deliberation between progressives of all parties”.

Burnham has championed many of Compass’s ideas in recent years, including introducing proportional representation and encouraging more cross-party collaboration. Some on the left believe this is the most rational response to the splintering of the leftwing vote, with the Greens having doubled their poll rating since the beginning of last year.

Others, however, believe Labour should be willing to fight the Green threat head-on, challenging the party over issues including the economy, national security and antisemitism. They point out that as the Greens have grown in support, they have attracted many from the Corbynite wing of the Labour party, from which Starmer wrested control to become leader.

Attention is likely to focus on Burnham in the days after this week’s elections as one of three likely challengers to Starmer, with the former deputy prime minister Angela Rayner and the health secretary, Wes Streeting, as the others.

Unlike the other two, Burnham would first need to win a Westminster seat, something he was denied the chance to do earlier this year when Labour’s ruling national executive committee said he could not stand in Gorton and Denton.