There will be cross-party cooperation on Brexit, whether their leaders acknowledge it now or not

In the end, most Labour MPs would rather have whatever deal the prime minister can negotiate than a no-deal Brexit

When people say there is no majority in the Commons for a no-deal Brexit, what they mean is that there is a majority for almost any deal (Reuters)

In the days after the European referendum, while political leaders were still in shock, some of them suggested that Britain might need a cross-party approach to leaving the EU. Peter Mandelson and Yvette Cooper said that the Conservatives would not be able to manage Brexit on their own.

So it has turned out, although it has taken two years and a botched election to prove it. The all-day cabinet meeting at Chequers last week was historic. Theresa May’s Brexit model merely set out the implications of what had already been agreed – in particular, the “backstop” terms for the Irish border – but it was the point at which people had to decide. It was one of those subterranean shifts when British politics realigned.

David Davis and Boris Johnson’s resignations were only the outward show of this change. As Daniel Finkelstein wrote in The Times, they resigned because they had “simply given up”.

They had no alternative to the prime minister’s plan, so they quit because they realised, eight months later, that they could not accept the open Irish border which they had agreed in December.

The fury of the Brexit irreconcilables was finally unleashed. Theresa May was braced for the onslaught, and she knew – because she can count – that she could survive it. She had also taken the precaution, I am told, of sending a message to European capitals asking them not to shoot down the Chequers deal straight away. They didn’t, which is a hopeful sign.

But the ferocity of the cries of betrayal was still shocking, and tempted some Tory irreconcilables – who cannot count – to think they could get rid of her.

Help was at hand in the unlikely form of a graceless interview with the president of the US, who told The Sun she had done Brexit all wrong: “I actually told Theresa May how to do it but she didn’t agree, she didn’t listen to me.”

Even Trump realised he had gone too far and apologised, a procedure that caused him such dissonance that his news conference with May the next day was a Jekyll-and-Hyde performance.

Dr Jekyll read out a prepared text saying the US still hoped to do a UK trade deal, but when he mentioned Brexit, Mr Hyde interjected: “I don’t know what they’re going to do, but whatever you do is okay with me … we will see how that goes.”

Trump did May a huge favour. His discourtesy helped discredit his friend Johnson and helped galvanise those who want to hug the EU close after Brexit. Given that three-quarters of the British people have a negative view of Trump, his attack on May’s handling of Brexit helped the realignment by which a large chunk of Remainers realise that the Chequers model is their best hope.

This applies to Tory and Labour MPs alike. Remember that most Tory MPs voted Remain, and that most Labour MPs don’t share Jeremy Corbyn’s historical Euroscepticism.

Some Labour MPs who paid close attention to the Chequers statement and Thursday’s white paper point out that it meets the six tests set by Keir Starmer, the shadow Brexit secretary. Or, given that one of them is to obtain the “exact same benefits” of EU membership, it comes as close as possible to meeting them.

So while Corbyn might never vote for a Brexit that keeps EU rules banning state aid to industry, most of his MPs might come to a different view when facing the moment of decision.

This is what must be borne in mind whenever it is observed that there is no majority for any kind of Brexit in the House of Commons. There may not be but, at each stage, when MPs are presented with a binary choice, there has to be a majority for one or the other.

The final vote will come down to a choice between a deal and no deal. And when people say there is no majority in the Commons for a no-deal Brexit, what they mean is that there is a majority for almost any deal, even if it means accepting free movement between the UK and EU.

If David Davis were serious about constructing a decision tree – his favourite aid to logical thinking, according to his friend Paul Goodman of Conservative Home – he would see that the Chequers model is the best of the range of realistic outcomes.

It is bound to be modified in negotiations with the EU before October, but even then most Tory MPs and most Labour MPs ought to prefer it to the rigours of leaving the EU without a deal.

Peter Mandelson and Yvette Cooper were right to call for cross-party cooperation two years ago. It is going to happen, whether the leaders of either party acknowledge it or not.

With the loss of her irreconcilables, Theresa May needs Labour votes to get whatever Brexit deal she negotiates through the Commons. Who knows how many Tory MPs would rather leave without a deal – 80, 100. It could be anything up to 158, or half her parliamentary party. Easily enough to wipe out her tiny majority. But there will always be enough Labour MPs willing to put what they see as the national interest first.

Labour MPs know they cannot force a general election, so we will have, temporarily at least, a government of national unity. The new centre party, an alliance of pro-EU Tories and Labour pragmatists, has not yet been formed, but we are already relying on it to save us from a no-deal Brexit.