Just another day in Brexit deadlock, as the prime minister rose to address the parliament she had so brutishly insulted with her demagogic “I am on your side” attempt to speak to “the people” over MPs’ heads. No apology, but she came to admit that her deal was in the quicksands, sinking fast, and she dared not bring it back for another trouncing. She is where she put herself, disgracefully in hock to the bigots and bullies of the Democratic Unionist party, who act against the will of remain-majority Northern Irish voters. Jeremy Corbyn was polite to call this “a national embarrassment”: this is far, far worse than a few blushes.

For parliament to seize control would, May wrongly claimed, set a dangerous precedent

What happens next, no one knows. Rigid as ever, Theresa May will whip her MPs against a well-backed amendment to hold indicative votes on Wednesday. For parliament to seize control would, she wrongly claimed, set a dangerous precedent. It does no such thing, when there is no government and only parliament to rescue us.

From the prime minister came no offer to resign in exchange for MPs passing her deal – confounding hot rumours. Nor did her cabinet turn Brutus and Cassius on this Ides of March, as foretold by the Sunday Times – which said 11 anonymous cowards in her cabinet swore blind they would do the deed. Instead of a coup, not a mouse’s squeak – not yet.

Why? Because this gang of rivalrous contenders ignore the crisis, eyeing one another to see who makes the first move, afraid of the old Tory adage that he who wields the knife never wears the crown: think Michael Heseltine. And, while thinking of Heseltine (who writes in today’s pages), just consider the puny array of microbes lining up for the contest, in comparison with the likes of him or Ken Clarke, both of whom make mincement of this lot with their every speech. Both were future leaders once, who would have changed their party’s Euro-obsessed trajectory, and both were rejected for the same bad reason that the Tories will again select a leader only on their extreme Europhobic credentials. Yet again, decent, moderate, constructive candidates will be ruled out, including the three women driven away already into the no man’s land of the Independent Group.

Theresa May is effectively gone. She is a leader in name only | Michael Heseltine Read more

In cabinet, a good example of how these minnows will put the country in peril to parade their own Europhobia was offered by Jeremy Hunt, who suggested May’s deal be held back to 10 April, for a lethal precipice vote. Others around the table made short shrift of his crude showing-off.

Yet one vital change came today – and May repeated it in the Commons. She has at last ruled out a no-deal crash. Another of her red lines bit the dust – but if only she had done this from day one. Too many times to count, she has repeated the nonsense that “no deal is better than a bad deal”. She even wrote this idiocy into her manifesto, but finally she told cabinet and Commons today that she will not let it happen.

Only leaders taking leave of their senses – or wanting to pull the House down as they depart – would willingly take personal responsibility for the ensuing disaster. The civil service reports to May in daily bulletins the emergencies they cannot prevent, as leaked to the Guardian last week: if just a few of these no-deal disasters came to pass, the government would be plunged into immediate crisis.

Yet those no-dealers will not go quietly. They stay in denial about what no deal means, ignoring warnings that trading on WTO terms will be calamitous – even from the likes of Pascal Lamy, a former WTO head. Extreme leavers are like those who drowned when they laughed at Noah’s flood warnings – to follow Boris Johnson’s latest biblical motif, though casting himself as Moses today took even his hubris to new levels.

Play Video 2:30 Not enough parliamentary support to hold third Brexit vote, says Theresa May – video

The indicative votes will happen, with more than 120 MPs signing the motion. But if these do lead to some compromise a majority can agree, May refuses to say she will adopt it. Not if it contradicts her manifesto pledges of no customs union; no single market. Obstinate even now, she can rub out some red lines, but only those that suit her whim. She pledged over a hundred times that Britain would Brexit on 29 March – but now we won’t. She still uses threats: a very long extension with EU elections, she warns her deplorables; she even mentions a referendum. But she refuses to commit to obeying the will of parliament if it constructs a plan. If that’s the next impasse, the only solution must be to put that plan directly to the people.

Any parliamentary agreement would be for a softer Brexit, with customs union and single market, but May would still refuse to face down her minority ERG adamants. Why? Since they are about to defenestrate her, since all that the unites her party is their intense contempt for their leader, why doesn’t she abandon them and help the Commons find a compromise? Her guiding ideal has been party unity – but that vanished long ago. Brexit has broken what was left of it, and it’s high time the Conservatives recognised they are no longer a party. No values bind together the beastly Mark Francois with the honourable Dominic Grieve; the narcissists Jacob Rees-Mogg and Johnson with Clarke and Heseltine.

The sooner the Tories realise their party is over, the better it will be for the country. Either there will be a referendum that will break them apart or some slow Brexit, with a long transition and perpetual negotiation that will drag on until it snaps in pieces. Divorce is necessary. Any future the Independent Group has rests with attracting a great swath of pro-European Tories to their cause, letting a Tory/Ukip rump see how it fares electorally when left to stew in their own Euro-obsessions.

The prime minister has been using the UK taking part in European elections in May as a threat. Everyone else should see this as the great opportunity. If Saturday’s million marchers fail to win a referendum now, those elections should be used as the great leave-remain national contest. It might split May’s party – could they stand on one manifesto? – though it would unite Labour under a clear remain banner.

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The latest British Social Attitudes survey from John Curtice finds leave/remain the true political divide, polarisation deeper and more passionate than at the referendum and far outstripping party loyalties. Some 40% feel strongly about Brexit from both sides, but only 8% report an equally strong passion for a political party. Class now is no predictor of political party affiliation, he finds; but age and education, closely linked with the old being less educated, are the leave/remain dividers.

With or without European elections, the Brexit rift will last for a generation unless a healing referendum lets voters have the final say on whatever brand of Brexit parliament agrees. Only the voters themselves can end the great dispute: without a vote, all who enable a damaging Brexit without public consent should consider how they and their party will suffer the political consequences for years to come.

• Polly Toynbee is a Guardian columnist