In Salzburg on Wednesday the sound of Brexit may be reassuringly anodyne, to ease Maria von May through a perilous Tory party conference. Climb every mountain and agreement is somewhere up there, will be the reassuring message from her ”few minutes over dinner” address to the 27 EU leaders. Only when – or if – she survives contact with her party will they put her impossible demands through the wringer.

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Every path looks blocked, every likely or unlikely deal set to be voted down in parliament. Emily Thornberry, the shadow foreign secretary, says Labour will vote down any deal that crosses its six red lines. Remember those were all drawn from promises the Brexiteers made in the referendum campaign. That includes their pledge to keep the “exact same benefits” of the single market and customs union. If that’s impossible, so were all the fantasies sold to voters.

Labour, gathering in Liverpool this weekend, faces its own great conundrums. Here’s its choice: it could emerge as the one party that can rescue the country from the morass the Tories have plunged us into, the one clear route out of both Brexit and austerity. Or it could descend into a hornets’ nest of internal strife incomprehensible to voters it needs to win over. A party at war over changing the rules to make every MP face an open contest at every election, obliging obedience to their local party, is a terrible look. It’s a rum democracy that refuses to propose US-style open primaries where local voters choose their candidate – the way the excellent Sarah Wollaston was selected in Totnes. Cracks run through the party, with new splits among Momentum people, and between Momentum and the unions, over new rules for selecting the leader.

Nor is there unity among non-Corbynites, ranging from a tiny handful who might split, to a large soft-left of many hues who only coalesce when respected MPs come under assault from the hard left. Chris Williamson, witch-finder general, stirring up enmity in his threatening “roadshow” tour of seats of MPs he thinks insufficiently loyal to the leader, may not be organised by the leadership, but he could have been stopped. It did step in when Canterbury’s Rosie Duffield risked a no-confidence vote for attending an antisemitism rally: outrage at threats to a very popular victor of an unexpected seat saw them shut down within hours. But she was left shattered, considering her future in politics – as are many others, distraught at the bile flowing through their party.

In his speech, let’s hear Jeremy Corbyn say something like this: “I will stand for no more vendettas against those who didn’t choose me as leader. Anyone using #JC4PM to abuse other Labour people, you don’t do that in my name. We are always a broad church – I know it better than anyone – and as a broad church, not as narrow sectarians, we will win.” That would be wise peacemaking, when any anti-Corbynites mad enough to split may vanish into the wilderness, but could still prevent a Labour victory.

Here’s the question for Corbyn: after a disastrous summer of feuding over antisemitism, will Labour spend the week on display as a nasty party energised by who controls its own meaningless citadels of power – or a serious party heading for real power?

Internal ructions are of Labour’s own devising, but it was never Labour’s fault that Brexit was destined to cause it agonies: how does it please its voters in Hampstead and Hull? Finally, a path through is emerging. As Brexit destroys the Tories – every deal, let alone no deal, looking worse than the next – this is Labour’s moment to step up as national saviour.

Facebook Twitter Pinterest ‘In his speech, let’s hear Jeremy Corbyn say something like this: “I will stand for no more vendettas against those who didn’t choose me as leader.”’ Photograph: Jane Barlow/PA

More motions calling for a people’s vote have been put to the conference than for any other issue, mostly from Momentum-backed constituencies. The leadership clings to the formula that when all Brexit options fail in parliament, Labour wants an election. Well, of course it does, but even if the Tories are crazy, the one thing they won’t do is gift an election to Labour. So far, Labour and the unions have put the people’s vote “on the table”. The conference has this chance to turn it into Labour’s first option.

Nervous Labour shadow cabinet members tell me the time isn’t right. Although 100 constituencies have swung from Brexit to remain, the polls are still not flowing fast enough. What if they declare for a democratic vote, and there is an election? A new Labour government would be forced into a deeply unwanted referendum. But there won’t be an election. Better by far to lead the upsurge of support for a popular vote that is coming from left and right of the party. The Tories have made such a mess of Brexit that “let the people decide” should be an easy message.

To all who say it’s an undemocratic rerun, here are some good analogies. If a trade union leader calls a ballot and members vote to strike, when he negotiates with the bosses he brings them back a possible deal: he doesn’t impose it, but puts it back to the vote. A GP says you need an operation and sends you to a consultant, who, being more expert, gives you odds of success and reckons it will do more harm than good: you would change your mind, wouldn’t you? If you agree to buy a house, before you complete you have it surveyed. If the surveyor finds foundations sinking, dry rot in the attic and dodgy title deeds, you change your mind. Well, the Brexit surveys are in and each looks grimmer than the last.

Let’s play optimistic politics. Corbyn should say: “We gave them every chance to produce the Brexit they promised. The endgame is here, but their Brexit promises have vanished. Now only a people’s vote can restore public trust – and only Labour can protect the country against Brexit damage.” That’s the victory path. Can he do that?

For any delegates at the conference tempted by factional warfare, just keep focused on the prospect of a second decade of Torydom. Sajid Javid – regarded as a “moderate” – regaled the last cabinet meeting with a 10-minute leadership pitch worthy of his Ayn Rand spirit-guide. He called for “shock-and-awe” tax cuts for business, deregulation of workers’ rights, abolishing automatic enrolment in pension schemes and scrapping environment controls.

That should knock sense into any Labour sectarians. So too should the success John McDonnell has had in recent weeks laying out policies and principles with the vigour of a man who seriously wants to win. Good to see him espouse the long-needed Robin Hood tax, which Britain has blocked the EU from imposing on financial transactions. He is making surprising friends: Lord O’Neill (ex-Goldman Sachs chief economist) told the Sunday Times: “I find myself struggling to be that scared by the prospect of a Corbyn government. They have captured the mood of the times.” The goal is wide open – if Labour avoids being its own worst enemy.

• Polly Toynbee is a Guardian columnist