If your signature policy – indeed, only visible political position – is to stop Brexit, and you claim that you will do absolutely everything within your power to prevent no deal, then it’s something of an error to suddenly introduce an exception. And yet this is the fatal mistake the Liberal Democrats have made.

When Jeremy Corbyn wrote a letter putting himself forward as a transitional prime minister purely to block no deal, extend article 50 and call an election, Lib Dem leader Jo Swinson could have welcomed the move as constructive, as the SNP, Greens, Plaid Cymru have done, with several Tory backbenchers prepared to talk, too. Instead, Swinson revealed that while the Lib Dems had been willing to prop David Cameron up for five years, implementing massive cuts and trebling tuition fees, she’s not prepared to countenance supporting Corbyn for five weeks solely to stop a disorderly exit from the EU. Her plan to do a backroom deal to put Harriet Harman or Ken Clarke in No 10 smacks not only of establishment stitch-up – it is also a constitutional nonsense, given it falls to the leader of the opposition, who has twice won a democratic mandate from his party membership and whose party won 40% of the vote just two years ago, to construct an alternative government. But constitutional nonsense, otherwise known as the Fixed-term Parliaments Act – which is itself another Lib Dem gift to the nation – is why we’re in this mess in the first place.

Labour’s plan has achieved a number of things. Corbyn’s supporters have long been compared to a cult, but the cult-like qualities of his opponents are rarely discussed. We can now see who is primarily motivated by stopping Brexit, and who is mostly driven by stopping Corbyn. In the coming weeks, pressure can be put on MPs as to whether their vendetta against the Labour leader is worth throwing Britain off a no-deal cliff for.

It has also put Labour on the front foot over Brexit, underlined by various positive newspaper front-page splashes. Brexit is an instrument of torture for Labour: its leading figures fret about maintaining and extending the coalition of remain and leave voters that deprived the Tories of their majority two years ago, and they differ on strategy going forward. Morale has been poor at the top, partly because of a weak response to Boris Johnson’s ascent to power. There has been some fatalism, too: a sense that Labour can only cut through during party conference or an election campaign. That’s been turned around: a route map for winning back disillusioned remainers from the Lib Dems has appeared – which is important, given Tory strategist Dominic Cummings is counting on a divided anti-Tory vote to secure a Johnson majority. During an election campaign, Labour will be offering a referendum with remain on the ballot paper, alongside transformative popular domestic policies such as taxing the rich to end austerity, scrapping tuition fees, and public ownership. The Lib Dems will be stuck as a single-issue party, any potential radicalism stymied by the fact that nearly all their target seats can only be won by winning over Tory voters.

But Labour still faces multiple challenges. The debate is currently focused on the danger of the Tories calling an election for Friday 1 November, hours after a no-deal has happened: a democratic outrage, making an outcome no one voted for in 2016 a fait accompli, whichever party triumphs. But if they break the convention of holding an election on a Thursday, the Tories could call one for 30 October and tell the electorate that voting for them would mean Brexit happening within 24 hours. That would help neutralise the Brexit party threat, complicate Labour’s attempts to avoid any campaign becoming a re-run of the referendum and – combined with spending commitments – represent a potent electoral threat.

Yet all Labour can realistically do now is attempt to bring down the government, prevent no deal and engineer an election. It will go into that election committed to a referendum with remain as an option. It has already seen how Lib Demmery – revived purely on the basis of Brexit – can be driven back. The hope must be that clarity on Brexit will buy the party permission to talk about a domestic agenda popular with a public weary of cuts and market fundamentalism. The party should be brave, offering radical policies that go beyond the 2017 manifesto, picking fights with vested interests as it does so. There are no guarantees about the result, of course. But Labour starts from a stronger position than it did when Theresa May attempted to wipe it out as an electoral force in 2017. Corbyn’s opponents make the mistake of continually underestimating him. They may come to regret it.

• Owen Jones is a Guardian columnist