With the Conservatives ready to seal an electoral pact with Nigel Farage, British politics has become a battle of cultures and beliefs. At the same time, as Labour’s shadow cabinet was forced to accept last week, we are now seeing a four-way fragmentation of the party system.

As a result, at some time between now and its September conference, the Labour party is likely to commit unconditionally to a remain/reform position on Europe. Whether via a second referendum, or – which looks more likely – a snap election, Labour’s task is to become the leading force within a progressive majority that wants to stop no deal, defend parliamentary democracy and halt the Trumpification of politics.

But it won’t be easy. A significant number of pro-Corbyn activists have convinced themselves that the demand for a second referendum is simply a weapon invented by Blairites to destroy the leader. Meanwhile, among a group of Labour MPs in former industrial constituencies and their voters and activists, there is no appetite for a second referendum that could sour an already bitter political atmosphere in their communities.

But the change must happen, and those like me, who have advocated it, have the duty to explain the risks, the penalties, and how they could be overcome.

Jeremy Corbyn’s attempt to deflect the cultural polarisation around Brexit by pulling voters towards a radical economic agenda was admirable – but it has failed.

It will no longer work while the Brexit issue dominates the debate. For every voter Labour is currently losing to Farage, it loses four to the Greens, Liberal Democrats or left nationalist parties. That was the evidence presented to the shadow cabinet.

Those within the Labour hierarchy still resisting change suggest that, if it flips now to remain, the party will test the loyalty of the so-called Labour leave voters, who have stuck with the party on the grounds that it “respects the referendum result”. Meanwhile, because remain votes pile up in big cities, even if it claws many remainers back, that’s not enough to compensate in the crucial marginal seats.

I have to admit this risk is real. But let’s consider the alternatives. If the incoming Tory leader tries, yet again, to put the old withdrawal agreement to parliament before 31 October, and if Labour was prepared to offer a free vote to MPs such as Caroline Flint, Gareth Snell and Lisa Nandy, a softish Brexit might be achieved, and two-party politics (in England at least) might reappear.

The problem is, for the Labour MPs who want to vote for a deal, a free vote is not enough. They need Labour to be able to “take the credit” for sorting Brexit out. But what looks like credit in Wigan looks like blame in Bristol, so there is no chance of persuading Labour’s leaders to put their fingerprints on a deal. Another alternative would be for Labour to begin a long summer “listening exercise”, letting its remain wing – Starmer, Watson, the Welsh and Scottish Labour parties and the Love Socialism Hate Brexit group – do its own thing while Corbyn’s inner team focuses on avoiding the issue.

That would ensure the September party conference was a bloodbath. The only way the membership could be stopped from overturning the present line would be if an army of union bureaucrats were deployed to neutralise conference democracy. The incoming Tory leader would get two months to set the agenda, with no parliament to worry about and Labour absorbed in an argument with itself.

The only realistic course of action is for Corbyn to come out, fast and strong, with a call to stop the Brexit chaos and rebuild Britain instead. Any advisers and shadow ministers who cannot sell the new position enthusiastically need to step back so that others can.

Labour has to demonstrate that it understands the situation has changed. It could say: “We tried to stop a divide opening among the British electorate, because leave and remain voters have more in common than what divides them. But we failed – and now we face a battle for the soul of Britain.” In that fight, there is only one side we can be on: with those fighting for an open, tolerant and globally connected country, against bigotry and a power grab by the rightwing elite.

But the most vital task is to reframe Labour’s offer to voters in leave-supporting areas. Polling shows that the most salient issue for these voters, after Brexit, is the NHS, followed closely by the economy and immigration.

Framing a no-deal Brexit as a threat to the future of state-funded healthcare should be easy, since President Trump, in one brainless soundbite, provided ammunition that will haunt the Tories at election time. Whether it’s Hunt, Gove or Johnson, the blunt question – will you rule out American ownership of our NHS hospitals after Brexit? – could be a killer one.

On the economy, the catastrophes at Ford Bridgend, British Steel in Scunthorpe and Honda Swindon should be made the centrepiece of an argument that only Labour, by halting the slide to no deal, can save what’s left of British industry. Alongside that, Labour must start turning its commitments on industrial strategy into concrete, local offers. The plan for a national investment bank, for instance, needs to be translated down to constituency level: Wigan, Sunderland and Stoke-on-Trent will get so many billion pounds each over five years, and we’re calling a local summit to ask what you want it spent on.

Finally, on immigration, Labour should commit overtly to the reform of freedom of movement once article 50 is revoked. Fair application of the existing rules could include strong regulations to prevent migrant-only hiring practices, a big migrant impact fund, plus the introduction of time limits for European citizens who do not find work in Britain, such as exists in Denmark.

If Labour makes this change, then for a few diehard Lexiteers it will feel, for a few days, as if their heads just exploded. But realigning Labour to the priorities of the progressive majority of British voters is obligatory.

We have only months to prevent the permanent fragmentation of politics. Labour is not only susceptible to its middle-class vote bleeding to the Lib Dems, but its left and youthful vote switching to the Greens. It is unlikely Labour will remain immune to the “green wave” sweeping Europe for much longer.

Strategically, Corbynism was the answer to a problem that was clear four years ago: Labour’s failure to fight austerity and war. Now the problem has changed, so the strategy has to change.

We have to give progressive voters a reason to come back to Labour – and urgently, before the habit of voting for others sets in.

Given the scale of the xenophobic swing on the right of British politics, an alliance of the left and the centre against Brexit is inevitable. The only questions remaining are who will set the terms of that alliance, who will inspire it, who will lead it – and who will own its success?

• Paul Mason is a writer and broadcaster on economics and social justice