Theresa May has only one way forward tomorrow. If she loses yet another Brexit vote, she must immediately offer one she can win. She knows well what that is, as Labour’s Jeremy Corbyn has left her in no doubt. It would propose leaving the EU on 29 March, in accordance with the referendum result, but remain in Europe’s customs union. If doing so requires a suspension of article 50 of the EU treaty, she should fly at once to Brussels to request it. Otherwise she should resign at once in favour of someone who will.

The strategy of squaring the circle on the Northern Irish border has failed. So have the farcical efforts of pro-Brexit MPs to find “alternative arrangements”. A border is not just paperwork. It is a complete edifice of differential tariffs, standards and controls, however structured and administered. The hard Brexit case that leaving the customs union need not harm British industry, agriculture, distribution and commerce has been overwhelmingly dismissed by all these areas of the economy.

MPs have a duty to the nation not to use parliament for personal prejudice or fantasy. They have a duty to listen to those who know. Just now, they are not fit to be MPs. There is no majority in the country for hard Brexit, any more than there is in Northern Ireland for a hard border. For the UK to abandon Europe’s collective economic community passes all comprehension. For buccaneer Brexiters, insistence on leaving the customs union (which has nothing to do with immigration) was always a bridge too far. It is a sign of their weakness that they now dare not compromise, even if it destroys their prime minister.

May cannot deny parliamentary reality. She is about to lose the confidence of the house on the great issue of the moment. Only dropping the “red lines” to which she foolishly committed herself in 2016 will pass muster. If she cannot persuade her backwoodsmen to vote with her, she must change tack and ask Corbyn to do so. That humiliating predicament is entirely her fault. It will be Corbyn’s duty to help the country through this crisis by supporting her.

Corbyn, and some of her own MPs, may demand that in return she agree to stand down. This is absurd. The prime minister must be able to take a customs union to Brussels as the head of government with ongoing parliamentary support – otherwise the deal will be meaningless. Suppose a replacement government entered negotiations under a Tory leader committed to hard Brexit?

For the time being May must keep control of the process. That is why she must bring forward a customs union motion that can win. Only if she refuses should she make way for a leader who will.

• Simon Jenkins is a Guardian columnist