Brexit is the disrupter that breaks things and shape-shifts as it scythes through the political life of the nation. Look at its unexpected landing zone this week after the Liberal Democrat conference. The Tories and the Lib Dems have adopted two startlingly extreme positions – Boris Johnson heading for no deal, damn the consequences, versus Jo Swinson’s revoke now, to hell with the will of the people. Both stands are alarming: one ignoring the economic fate of the nation, the other risking riots over the denial of democracy.

Suddenly Labour is the moderate, thoughtful one: only another referendum has the authority to abandon or confirm the decision of the first, after three years of hellish impasse. If Swinson was trying to position the Lib Dems midway between the extremes of Hulk Johnson and Corbynism, her revoke blunder takes her party out on another distant limb. Her abrasive rejection of ever working with Jeremy Corbyn is another error: her better role should be as enabler, bringer together a progressive alliance. Caroline Lucas does that tone well.

For Labour to emerge next week as the party with the best Brexit policy, it must push for a referendum immediately

For Labour, at its Brighton conference next weekend, Swinson has opened up a golden opportunity, a chance to forget past prevarications. Labour’s Brexit ditherings have often infuriated the majority of its voters who are remainers, from Corbyn’s virtual no-show during the referendum campaign, to weak fence-sitting, trying to hold together with northern MPs in leave seats. Tens of thousands of Labour members have fled – some among the 30,000 remainers recently joining the Lib Dems.

For Labour to emerge next week as the party with the best Brexit policy, it must push for a referendum immediately: head-counters in parliament suggest there could now be enough MPs to back a people’s vote after the Tory evictions, with Oliver Letwin and others in support. No need for the usual five months: if general elections are fought in 25 working days, so could a referendum if parliament voted it. The choice on the ballot would be between remain or whatever deal was agreed by then, probably still May’s. With Brexit resolved before an election, parties would lay out more realistic manifestos for the future.

If MPs don’t back a referendum and an election follows, only Labour will offer voters that final referendum say. The policy will be to try to renegotiate a better, closer relationship with the EU and to put those terms on the ballot paper. Crucially the Labour leadership would back remain.

Facebook Twitter Pinterest ‘The unity of all remainers must hold fast.’ Jeremy Corbyn at Fife Jobs Rally last Saturday. Photograph: Ken Jack/Getty Images

This has been unjustly mocked: what, renegotiate and then vote against your own deal? But that is entirely rational. Make the deal as good as it can be – if leave wins again, it would be implemented. But no Brexit is a good Brexit, and Labour would this time lead the progressive parties’ fight to persuade the country to remain, advocating EU reforms if we stay. Some Labour MPs would take the leave side: the party should be tolerant, as Harold Wilson was in the 1975 referendum, with no need for a Johnsonian expulsion of dissidents.

This referendum-remain-reform motion is backed by John McDonnell, Keir Starmer, Emily Thornberry, Tom Watson, Diane Abbott, Andy McDonald and most of the shadow cabinet. An unequivocal conference motion will halt the desertion of Labour remainers to the Lib Dems, making the other two parties look extreme.

To be sure, there may be only modest popular appetite for another vote: many hearts sink at a rerun of that nation-scarring calamity. But confronted with the brutal “out” or “revoke” alternatives offered by Johnson and Swinson, it will seem the better way to resolve this crisis. Peace and healing is unlikely, but it would bring acceptance from both sides, whatever the result.

The next referendum will be a more honest fight. How much easier to combat Brexiters with a concrete deal on the table for close dissection, where it can be exposed, item by item, as so much worse than the freedoms we have now within the European Union. This time the campaign is better prepared to extol the value of the EU, better armed for combat with unicorn promises and mendacious threats of Turkish invasions.

Labour cannot out-remain the Lib Dems. Thankfully, it doesn’t need to | Tom Kibasi Read more

But here’s Labour’s risk. The Unite general secretary, Len McCluskey, some other unions, some shadow cabinet leavers and controllers of blocks of delegates, back a conference motion that’s absurdly impossible to sustain: they would hold a general election, negotiate a new deal and only after that negotiation would the party decide whether to back leave or remain, or to stay neutral in a referendum. Neutral! Imagine sending Labour campaigners out door-knocking in the coming election to advocate a referendum but unable to say how the party would vote on this critical issue. Surely the Labour conference will have none of it.

Meanwhile Johnson might, just, pull off a deal, though every hint suggests something even worse than May’s plan. Despite DUP objections, a Northern Ireland-only deal would be great for Belfast – making it the new Dublin, a magnet for investment if it stayed in the single market and customs union. But it would be terrible for the rest of the UK, excluded from the customs union that the May deal keeps us in. An open border in Ireland would be bought at the expense of hard-as-rock borders all around the rest of the UK. Scotland would rightly demand the same as Northern Ireland, or leave.

The risk is that sheer exhaustion will make any rotten deal that the Hulk drags home look better than nothing. That’s when the unity of all remainers must hold fast: no party advantage-scoring, no absurd refusal to work with Corbyn, all ready to resist together any bad deal in that famous last ditch.

• Polly Toynbee is a Guardian columnist