Brexit is not really a matter of opinion. Of course, some people believe it a good idea: others, including me, think it a disaster. But as David Davis’s resignation today shows, that’s not now the point. It simply is not deliverable.

The only way Brexit might have worked without an economic collapse is the Norway model of close integration with the structure of the European customs union and single market without being part of the formal EU institutions.

In the end, after much anguish as she tried and failed to identify a workable “hard Brexit”, Theresa May recognised this. Hence her Chequers fudge, which was a decisive move towards Norway, with the clear intention to go further in negotiations. She tried to coax her party into a policy that kept the Brexit label but junked most of the Faragist content. At Chequers she, in effect, agreed alignment with the EU on swaths of economic regulation, accepting elements of jurisdiction by the European court of justice, crossing each and every one of her previous red lines.

But it hasn’t worked. As with the poll tax in its dying months, ever more elaborate fudges and “transition” and “interim” proposals can’t bridge a chasm of this size. If she tries to move further towards Norway, she loses her party; but if she doesn’t, she loses any possibility of a workable deal with the EU.

May is now in the desperate position of Anthony Eden after Suez and James Callaghan in the winter of discontent. She has no policy to govern or unite the country, and her party and government are imploding. Whether it takes days, weeks or months, her government is over – and Brexit too, unless it can be reconstituted under a new prime minister or government.

That now is the question facing parliament – and in particular my Labour party, which has a crucial part to play. Jeremy Corbyn needs to make it clear that he will not be a party to any Brexit. Hitherto he has declared opposition to “hard Brexit”; but since there now isn’t a workable soft Brexit, the political and economic necessity is for Labour to oppose Brexit entirely.

Corbyn hopes for a general election and entry into No 10. Maybe the government will implode to such a degree that this happens before the key parliamentary votes on Brexit. But if this doesn’t happen quickly – and I doubt that enough Tory MPs would vote for a motion of no confidence to bring it about – then the next best course is a people’s vote.

Precisely how and when a people’s vote can command a Commons majority depends upon whether May, or her Tory successor if she falls soon, is able to negotiate anything with Brussels. But since negotiations of some kind are likely to continue for a while, even if they fail, decision time will probably be at the end of the year. A people’s vote – with the choice being between staying in the EU, as against the Tory “bare bones” deal if there is one, or no deal if there isn’t – would then be in the first half of next year. Labour, with Tory pro-Europeans, would lead the campaign to stay in the EU.

The original sin of Brexit – the lies, contradictions, half-truths and omissions on which it was built – have come back to haunt the Thatcherite Tories who started all this with Nigel Farage and Ukip.

It is simply not possible to achieve the “freedom” from EU economic institutions that Brexiters want without undermining Britain’s economy and security. But anything short of hard Brexit leaves Britain exactly as Jacob Rees-Mogg has described it – “a vassal state”, a colony of France and Germany in key respects, because we are forced to follow their trade and regulatory systems without a seat at the table in devising them.

It is not often that I agree with Rees-Mogg. But on the imperative not to become a “vassal state”, I agree entirely. The fact that we would both fiercely oppose such an outcome demonstrates that it is politically non-viable and would not command a parliamentary majority.

The only way now to reassert British sovereignty and national interest is to vote to stay in the EU. We tried a different course. It hasn’t worked. It can’t be made to work. It is time to end this national farce and humiliation, and stop playing politics with people’s jobs and livelihoods.

• Andrew Adonis is a Labour peer