There’s what happened at the government's Brexit away day at Chequers last week and there’s what’s happening in the real world. The two appear to be very different.

In a well-briefed, high-detail take in today’s Sunday Times Tim Shipman paints a picture of a usually fractious cabinet that managed to come together in agreement at the PM’s country residence about the way forward on Brexit.

Each faction seems to have managed to throw its weight behind a plan produced on the day by Oliver Robbins, Britain’s chief negotiator. It states that the UK will:

● Demand mutual recognition of standards for goods traded between the UK and the EU.

● Make a public commitment that British standards will remain as high as those of the EU.

● Pledge to keep rules and regulations “substantially similar”.

● Insist upon the creation of a dispute mechanism to oversee areas where the UK wants to diverge from EU regulations — and that the European Court of Justice would have no role in it.

Both Boris Johnson and Philip Hammond, perhaps the two ministers furthest apart on Brexit, said they were able to support the proposals. This led one of their colleagues to joke that ‘if you both agree with it, there must be something wrong.’

The truth is, that’s no joke – there is something wrong. The bonhomie felt at Chequers wasn’t the emotion of a group of people realising they actually agreed with one another. It was driven by relief that an embarrassing barney, or a resignation, or even a fistfight, had been avoided. The idea that Hammond and Johnson are now on the same page, or can be kept on one in the months ahead, is for the birds.

Meanwhile, the real world keeps stubbornly intervening. Labour moderates have quietly been working away at Jeremy Corbyn to persuade him to support the idea of Britain remaining in a customs union. The Labour leader and his acolytes may be at ease with Brexit – and for very different reasons to Tory Leavers – but they have recently begun to show a willingness to play the ideological soft-shoe shuffle, bending their dogma for the sake of political ends. And with the Conservatives – especially on the backbenches – still heavily divided over our future relationship with the EU, they scent that a major victory, and a humiliation for the Government, could be on the cards.

Keir Starmer took to the Marr show today to make clear that Labour’s position, though still frustratingly vague, is shifting towards audacity. The Shadow Brexit Secretary suggested that Labour could support Tory MP Anna Soubry's customs union amendment, which would almost certainly give it a majority.

“Crunch time is coming for the Prime Minister. The majority in parliament needs to be heard and it will be heard sooner or later,” said Starmer.

Something must break, sooner or later. The scale of the challenge and the tenor of the times demand it. It remains unthinkable that a final deal can be reached that manages to keep Johnson and his like-minded divergers on board with the sizeable number of Tory backbenchers who grow ever more publicly rebellious and outspoken.

On The Wright Stuff last week, former culture minister Ed Vaizey let loose in dramatic fashion. The idea Brexit would be good for trade was “complete nonsense” and “fantasy land”, he said. “The idea we’re going to strike any new deals in the next few years is rubbish and [the idea] any of these free-trade deals are going to compensate for making it more difficult to trade with Ireland or France or Germany is also rubbish.”

Asked whether his remarks would get him into trouble with the party leadership, Vaizey was dismissive. “Discipline has completely broken down in the parliamentary party so no one tells anyone off because there’s no power anywhere. It’s an atomised parliament.”

Vaizey may no longer be a minister or at the heart of Tory power politics, but he undoubtedly speaks for those MPs growing ever more frustrated at the Johnson/Rees-Mogg attempts to drag the government towards a hard Brexit. The two positions cannot be reconciled, the personal relations that might smooth things over no longer exist, and the Conservative rebels have no compunction about voting with their principles rather than their party.

It should now be relatively easy for Labour to peel these rebels away from the government when it comes to some key votes. Labour’s parliamentary party - if not its leadership – remains overwhelmingly Europhile. If Corbyn can be persuaded or even forced to play hard politics on Brexit, he could bring down Theresa May, leave a gaping wound in the Tory party, and make his Labour a more palatable option for remainers and soft Brexiters across the country.