Keir Starmer is being urged to lay the groundwork for cooperating with the Liberal Democrats and Greens at the next general election, by MPs and campaigners who argue the party will struggle to win a majority alone. In a new report, called We Divide, They Conquer, the progressive pressure group Compass sets out the scale of the electoral challenge facing Starmer’s party after last year’s general election. It warns that Labour would need to achieve a swing of 10.52% – larger than Tony Blair’s in 1997 or Clement Attlee’s in 1945 – to win the 124 seats Starmer requires to secure a fragile majority of one. “The electoral facts point to one conclusion: Labour will struggle to win alone. So the party can choose to lose alone and remain in opposition, or build cross-party alliances, lead a new government and transform the democratic landscape,” the report says. While Boris Johnson’s Conservatives would need a swing of just 3.18% against them to lose their majority, the Lib Dems are in a better position to take some of the Tories’ most vulnerable seats. The report, written by the activists Grace Barnett and Neal Lawson, identifies 59 seats it calls “progressive tragedies”, where the combined vote of Labour and the Lib Dems would have been enough to beat the Conservatives and the Brexit party in 2019. They include London constituencies such as Wimbledon, Finchley and Golders Green, and Hendon as well as “red wall” seats such as Bury North, Derby North and Bolton North East. There is a history of fierce tribal enmity between Lib Dem and Labour activists at grassroots level, but the report highlights areas of policy agreement. These include a significant increase in green investment; reform or replacement of universal credit; ending rough sleeping, and reform or abolition of the House of Lords. But the authors argue that a commitment to backing a more proportional voting system would open the door to a much closer relationship with other progressive parties, which have long supported the idea. “Labour making a firm commitment to back PR would be a game changer for the Lib Dems and the Greens, incentivising them to campaign and vote tactically. This would make it easier for progressives to elect a Labour-led administration, with a big democratic mandate to introduce PR,” they say. During his leadership campaign, Starmer said: “We’ve got to address the fact that millions of people vote in safe seats and they feel their vote doesn’t count” – though he did not go on to spell out an alternative. Compass is setting up groups of activists in Labour, the Lib Dems and the Greens, who will work to establish cross-party links and cooperate on shared policy priorities. The Labour MP Clive Lewis will launch the report at an event on Monday alongside the Lib Dem MP and former leadership candidate Layla Moran, the Green MP Caroline Lucas, and the SNP MP Tommy Sheppard. Lewis described the current electoral system as “like a game of monopoly where the Tories are always the banker”. Asked how Labour’s leadership should be preparing to collaborate with other parties, he said: “It’s about humility: it’s about accepting that you don’t have a monopoly on wisdom. There are still so many people in the parliamentary Labour party who think, just with the right leader and the right policies we can win outright, and dictate the future. But the future isn’t going to be dictated, it’s going to be negotiated.” The Lib Dem leader, Ed Davey, has made clear his focus is on rebuilding the party after the bruising electoral defeat that saw his predecessor Jo Swinson lose her seat. But Lib Dem sources pointed out that the most plausible way of ejecting Johnson from Downing Street involved the Lib Dems, as well as Labour, taking seats from the Tories.