Byelections can change history, glorious victories and notorious defeats marking constituencies forever in the annals of political nerdery. Some results are freaks – the Liberals’ surprise win in Orpington in 1962 did not herald a great revival for the party, nor was Shirley Williams’s spectacular Crosby win in 1981 a harbinger of SDP mould-breaking. But sometimes byelections do signal seismic change.

Today Peterborough bids to crack open the old two-party hegemony, with the new Brexit party favourite to win. Labour may yet hang on, its campaign benefiting from an experienced get-out-our-vote local team. But even if Nigel Farage just misses, he can still claim an extraordinary result, rattling the Tories deeper into no-deal extremism. Glumly resigned to their coming humiliation, the party’s large foolish tendency will persuade themselves that Boris Johnson can magic them out of the slough of despond.

Brexit party eyes early breakthrough in Peterborough byelection Read more

Labour is the party standing to lose most if Peterborough slips its grasp. Though its former MP’s prison sentence has some effect, the real struggle is to push Jeremy Corbyn off the fence of Labour’s failed Brexit policy. Win or lose today, watch both sides in Labour leap out to claim victory/loss was due to their favoured policy. The battle is on to reshape Labour policy not just for a referendum but to commit to campaigning vigorously for remain. Another Europe is Possible, Hope not Hate, Best for Britain and others are hitting the phone banks, calling round local parties to back a strong referendum-and-remain motion for the party conference.

The anger and the anguish among Labour members is real, the party bleeding votes and members with every week that passes, while Corbyn’s position stays blurred and unchanged. A Focaldata poll of 15,000 voters in today’s Independent spells out that warning. In a general election now Labour would stand to lose 42% of those who voted for it in 2017, with 30% deserting to Lib Dems and Greens, 2% to Plaid Cymru and SNP, and just 10% defecting to the Brexit party. Without turning clearly to remain now, Labour won’t win a majority. It would be the biggest party, just, but any anti-Brexit parties – Lib Dem and nationalist – it allied with would demand a referendum and unflinching backing for remain.

Labour can’t afford to wait for its party conference in late September – and all but the knot of Lexiters surrounding Corbyn know it. The shock of the disastrous European election results is turning MPs towards the only direction that can rescue the party. Jenny Chapman, shadow minister for exiting the EU and MP for leave-voting Darlington, is a bellwether. Once an adamant anti-referendumite, on Wednesday she strongly backed another public vote on the BBC’s Politics Live. “Take the bull by the horns now” she said. “I don’t see any other way than a referendum.”

Other MPs equally conflicted by their constituents’ Brexit stance include Karl Turner, whose Hull East was a strong leave-voting seat. But he too has now switched to remain. “Yes, I would lose a few thousand votes but not enough to lose the seat. This policy is a disaster and I need to do what’s best for my constituents: I’m not their delegate.” He sees other Labour MPs now realising that even in leave seats, the loss of remain votes will do far more damage, and the very real prospect of a Tory no deal is terrifying. John McDonnell, on Wednesday night’s Peston programme, was even clearer than before: “Any deal has to be put to a public vote.”

How long can Labour resist coming out unequivocally for remain? After a week of Trump and D-day, next week Corbyn speaks to the PLP and the shadow cabinet meets, where there will be an urgent push to topple Corbyn off the fence, in order to summon back voters lost by obstinately pursuing a policy the great majority reject. Shadow cabinet members warn that Labour needs a strong clear pro-remain policy now, before the Tories select their new leader next month. September is far too late, but the membership will force the policy change: better by far Corbyn is seen to make that leap himself.

Jeremy Corbyn is right: Labour needs both its leavers and its remainers | Larry Elliott Read more

Here’s the curiosity in Labour’s position: all his life Corbyn followed the Bennite belief in the supremacy of party members to determine policy, yet now he defies them. Doubly odd is that he owes the security of his tenure entirely to that same membership who keep him there, despite his refusal to listen to them. Local parties report his perversely inert stance on Brexit is driving members away; those not tearing up their cards will show up as non-renewers. Michael Chessum, national organiser of the motion to conference, says: “It is time for Labour to make a final and complete shift towards backing a public vote and opposing Brexit. The alternative is that the electoral coalition behind Corbyn’s Labour falls apart.”

The Corbyn coterie tries to dismiss all critics as phantom “Blairites”, but this is the party’s left rebelling. They rightly see this as a fundamental culture war with the Trumpite alt-right, and demand “an agenda of internationalism, defending free movement and fighting for radical change rather than pandering to the nationalist right”. They see the Corbyn/Len McCluskey stand aligning with the right, clinging to an imaginary ideal of the perfect Labour voter as “old, white, male, with a regional accent” as if every other working Labour supporter doesn’t count. But they do, as poll after poll shows. Win or lose in Peterborough today, this is the battle not just for the heart of Labour but for its very survival. As one leader in the charge for the referendum-and-remain motion says: “Jeremy is MIA.”

When the Tories select a no-dealer, the country needs a powerful opposition to mobilise every vote against a reckless new prime minister willing to drag the country out of Europe without public consent.

• Polly Toynbee is a Guardian columnist