MPs from different wings of Labour have reopened the debate on a progressive alliance within the party.

Clive Lewis and Jon Cruddas have co-signed a letter in the Guardian calling for the reinstatement of three party members who were summarily expelled for supporting a National Health Action party candidate in Jeremy Hunt’s constituency at the last election. Nearly 30 other party members have backed the call.

Lewis is a frontbench Treasury spokesman on the left of the party, and Cruddas, a former aide to Tony Blair, has been a leading thinker in the party for most of the past decade.

Neal Lawson, who chairs the pressure group Compass, which campaigns for a progressive alliance, argues that cooperation with other progressive parties at last Thursday’s local elections could have tipped the balance in close-fought councils.

In the south London borough of Wandsworth, Labour came within a handful of votes of toppling the Conservatives. The Tories lost eight councillors, leaving Labour just seven seats away from what could have been a defining result for the party.

Campaigners also point to the Liberal Democrats’ victory in Richmond, where, with the Greens, they gained a total of 28 seats to win the council back for the first time since 2006.

In their letter, Cruddas and Lewis argue that a progressive alliance could have delivered as many as 60 seats for Labour at last year’s general election. That would have given Jeremy Corbyn a working majority in the Commons.

But Labour has long rejected all local arrangements with other parties. The three members in Hunt’s South West Surrey constituency who were expelled last year – Steve Williams, Kate Townsend and Robert Park – were not alone. In Hastings, a Labour party member, Nicholas Wilson, who campaigned against Amber Rudd on an anti-corruption ticket, was also expelled. He won more votes than Labour needed to unseat the former home secretary, who had a majority of 346.

Lawson said: “Politics in Britain is in a stalemate. Labour must give local parties the ability to negotiate progressive alliances as the best way to break the stalemate; it worked in 2017 and again in the local elections last week.”