So what now? Boris Johnson’s tactic of leaving Brexit to the last minute and then serving up a dog’s breakfast seems unlikely to work. Both Dublin and Brussels have effectively rubbished it. The offer to the EU is absurd. In place of Brexit’s promised “no border on the island of Ireland”, he offers two borders: a customs one on land and a regulatory one in the Irish sea. In place of “frictionless trade”, he offers a blizzard of bureaucracy and a gift to smuggling. In place of “take back control”, he offers a non-existent Northern Irish assembly a veto over British trade policy. As the prime minister’s first hesitant step into personal diplomacy, it is dire.

The only sensible way forward must now be to separate Brexit on 31 October from the resolution of these fiendish trading arrangements

But let’s stick to essentials. Johnson has rightly conceded that Northern Ireland should remain in an all-Ireland single regulatory zone, to honour the Good Friday agreement with the south. That is a relief. Yet he remains adamantly opposed to a customs union embracing the UK and the EU. This contradiction he submerges in a morass of costly technologies and checkpoints. Customs posts become “designated locations”. It is possible some type of “soft” border can be devised, but not by halfway through October. The nonsense of no customs union with no border has come home to roost.

The only sensible way forward must now be to separate Brexit on 31 October from the resolution of these fiendish trading arrangements. The UK should formally leave the EU on time, and draw Brexit’s poison from the British body politic. This means parking the fate of the ongoing customs union in the transition period, as under Theresa May’s deal. But that involves agreeing a framework for its eventual resolution. Here the ideal for everyone should be stop rabbiting on about borders, and for the EU to take a gamble on easing the backstop. Of course the Northern Ireland government should not have a veto, but the British parliament should. The backstop should go on ice.

That way the UK could leave the EU on 31 October and the 2016 referendum would be honoured. Over the British Isles would arise a deafening sigh of relief. Hard Brexiters could gird themselves for trade arguments to come, over border posts and regulatory alignments. Soft Brexiters could pray that a new British government might see sense, and opt to remain in the customs union and single market. Everyone could take a breather.

But such a deal, if the EU agreed it, would first have to pass through the valley of the shadow of the present Commons. Johnson needs 320 votes and he does not have them. His reckless contempt for the House of Commons last week made it near impossible for Jeremy Corbyn to collaborate. But both men owe it to the country to attempt to steer this crisis to resolution. Further chaos over the Benn Act aimed at preventing crashing out would be a nightmare. Any Brexit deal returned to the EU27 in two weeks’ time should go with a thumping majority.

Johnson’s negotiators now need to fudge everything except “leave on 31 October”. Corbyn in return would relinquish “leave on customs union terms”. Of these, the second is negotiable – at least over time. Johnson may not back down on his baffling hostility to the customs union, but he could agree to kicking the border issue into the transition period. Labour could honourably support a deal that left that option open, with its resolution “repatriated” to parliament.

Johnson’s Tory fundamentalists, wrapped as they are in the casuistry of no deal, may be appalled by him talking to Corbyn. He should weaponise his reputation as a turncoat and opportunist. Yes, the Tory European Research Group might turn on him. He should strip them of the whip. As for the Northern Irish DUP, their attitude is less certain. They have had a nasty shock, with opinion in the Ulster province emphatically against hard Brexit. For them Johnson’s virtual border is simply a savage cost.

As for Corbyn, he might lose the backing of the “rebel alliance” and of opposition referendum supporters. But he would no longer have round his neck the electoral albatross of opposing the will of the people. He would be rid of the Brexit incubus.

Leaving the EU was never about trade. If anything more than a howl of anti-liberal protest, it was about immigration. A desire to restore sovereignty to Britain’s political institutions was perfectly valid, and leaving the EU would contribute towards that. Brexit is indeed Brexit, but that does not make it about leaving customs unions and single markets.

When Thatcher negotiated the Single European Act in 1986, she rightly praised it is as a boon to free markets. Her subsequent reservations about a power-hungry EU might be seen as justifying Brexit, but not justifying a dismantled open market, as a hard Brexit proposes.

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There are many skeletons rattling in this cupboard. Some of those closest to Johnson seem exhilarated at the prospect of breaking the Benn Act, and moving Britain towards anarchy. They are dangerous. Some round Corbyn have a similar revolutionary purpose: that anything that damages the government must be good. This is the legacy of the new politics, to bring disruption to the heart of the constitution.

Johnson and Corbyn may not be stars in the firmament of British political history, but on them has fallen the burden of getting the country out of this mess. Johnson is a prime minister on a hook of his own making. The EU and Corbyn would do everyone a service by helping him off it. They should amend and approve the May deal. It should be yes to Brexit, but hard or soft Brexit – that’s for another day. The first move should come from Corbyn. He opposed no-deal Brexit. He should show us a yes-deal one.

• Simon Jenkins is a Guardian columnist