The British are great most of all in their pragmatism – or so much of the world once thought. The European Union’s supreme talent is for compromise – or so it was widely assumed. Both sides have much to lose from a ruinous version of Brexit and for that reason it will be avoided. This logic was the basis for believing that it could be managed in a way that contained the damage to trade, jobs and investment from extracting one of its largest members from the world’s most prosperous bloc.

The EU27 will suffer from a traumatically severe Brexit. For Britain, the consequences of departing without a deal would be several times more calamitous. The chief executive of one of our biggest ports recently told a private dinner that if the government was serious about planning for a “no deal” scenario and a hard trade border it would have to invest in 20 square kilometres of lorry parking at each major port. Rational minds must thus prevail. Some sort of bargain has to be struck. It will be just about OK in the end. This is the case I have often heard from the pragmatic majority in the cabinet when they have sought to persuade me that it will be sort of all right on the night.

That hope has not evaporated, but it is becoming increasingly less comfortable to be any sort of optimist about Brexit. The outlook is darkening. The sand is running through the hourglass. I hear more and more businesses say that they are contingency planning for a bad Brexit. Those ministers who still hope for the best now sound tight in the larynx when they try to voice reasons to remain cheerful.

It is more than six months since Theresa May dispatched her divorce letter. There have been five rounds of jaw-jaw in Brussels. The bargaining has still not advanced beyond square one. Michel Barnier, the EU’s main negotiator, describes a “very disturbing” deadlock. Philip Hammond publicly expresses fears of “a bad-tempered breakdown”, an outcome the chancellor then makes more likely when he clumsily characterises the EU as “the enemy”, an insult not much softened by his subsequent retraction. Mrs May once thought she would be travelling to this week’s Brussels summit to come away with an agreement that the talks could progress from the terms of the divorce settlement to negotiations about Britain’s future relationship with the EU27. This is not going to happen. Most diplomats on both sides think that the best she might get from the EU27 is some sort of agreement that they will start talking among themselves about what kind of transition arrangement they might be prepared to accept. December has become the new target month for concluding the first phase of the negotiations. This slippage prolongs the uncertainty for companies about the prospects for doing business in a post-Brexit Britain and encourages more employers to prepare for an ugly outcome. More boards will decide to switch investment and jobs away from Britain to less risky locations.

Who is to blame for this stalemate? The answer you get depends on where you put the question. From EU capitals, you hear the understandable contention that it is extremely hard to negotiate with Britain when its riven government hasn’t finished negotiating with itself. It doesn’t help that Mrs May is desperately weak. Recent events have compounded the impression that she is a lame duck, one crisis away from having the last crutch kicked from under her. Her hapless party conference speech was almost universally reported in the continental media as a metaphor for her enfeebled premiership. The daily tests of her authority by various Tory factions add to the impression of chronic debilitation. EU capitals noticed when Boris Johnson brazenly trampled over collective responsibility by publishing his own version of a hardline Brexit that openly contradicted the prime minister’s position. They further noticed that the foreign secretary didn’t get sacked for his impudent freelancing.

EU capitals also notice when senior Tories join more junior ones in demanding the head of Philip Hammond, one of the few in Mrs May’s cabinet to talk realistically about the hard choices that have to be faced to avoid plunging the economy into chaos. To anyone looking in on Britain from outside, it is another sign of Mrs May’s fragility that the government has been forced to postpone the committee stage of the withdrawal legislation, in this case because of the threat of rebellion on multiple fronts by pro-European Tory MPs.

None of this incentivises the EU to be terribly serious about the negotiations. All of it reinforces the view, in some European capitals and some elements of the commission, that it is essentially futile to try to find a way forward because Mrs May isn’t capable of enforcing any deal on her quarrelling cabinet and splintered party. Would you buy a car from someone who can’t describe what the car looks like, nor convince you that they actually own it? Key European players ask why they should spend any of their political capital trying to progress the negotiations when they can’t be confident that Mrs May will still be sitting on the other side of the table come Christmas.

By taking that attitude, they make her weaker. They chip at her authority over her party and her credibility with her country. They compound the problem of which they complain. People around the prime minister counter that it is the EU that is behaving with unreasonable rigidity and, in some respects, they have a point. One reason the negotiations can’t move on to trade is because they haven’t reached an agreement on the border between Northern Ireland and the Republic. But the status of the Irish border can only be settled once the future trading relationship is established. Which the EU won’t yet discuss. Catch-22.

A similar stalemate has frozen progress about Britain’s bill for checking out. As is so often the case in divorces, even breakups conducted with more goodwill than this painful separation, money is the biggest barrier to moving forward. Mrs May thought she had offered a substantial concession when she made her recent speech in Florence. She promised that Britain would meet its financial obligations to the EU and implied that there would be further payments in return for continued access to the single market on frictionless terms. Advisers to Mrs May argue that this speech demonstrated that she was being responsive to the EU and showed that she was a “grown-up” about the compromises that will be necessary to secure a deal.

She has also recognised that Britain will have to submit to adjudications by the European court of justice during a transition period, as well as accepting the continuation of freedom of movement for at least two years after 2019. Having taken these steps, at the risk of enraging the hard Brexiters in her party, the prime minister is hugely frustrated that there has been little reciprocation from the EU.

An important reason for that is an emerging split in the EU. Very credible sources report that Mr Barnier wanted to progress the talks, but has been blocked by some member states. The most powerful naysayer is Germany, which confounds the belief of some in the British government that Angela Merkel would ride to the rescue.

People intimately familiar with the state of the negotiations say that they have become jammed in a chicken and egg situation. The Germans aren’t prepared to move on trade until the British are more specific about the money. Mrs May can’t offer anything more on the money until the EU is prepared to respond with some movement on trade. Catch-22. Again.

The Germans would be wise to take note that the people most delighted with this deadlock are the Brexit zealots in the Conservative party who have always wanted, and continue to agitate for, the severest form of rupture with the EU. The Brextremists would love to kill off any transition period. They fear that the longer that Britain sits in a departure lounge, half in and half out of the EU, the more chance there could be that the country might change its mind about leaving or end up agreeing some kind of associate membership.

The Brexit fanatics crave a bad-tempered breakdown in the negotiations in the hope that this will be the precursor to the most stark form of departure. They want a breakdown to be blamed not on their own delusions and the fantasies that they peddled during the referendum. They want the guilty men to be Remainer saboteurs at home and dastardly continentals in Brussels and Berlin. The Germans might take note of that as well.

There is no majority in Britain for an extreme Brexit that hurls this country into the vortex. Nor is there a majority for an economically disastrous Brexit in parliament. A car-crash Brexit would be massively disruptive for much of the continent. It wouldn’t be a benign outcome for the EU either.

So the logical man still says that cool heads ought to prevail and a deal should be struck in the end. The flaw in the reasoning of the logical man is to assume that the world is always sane. Were you searching for ways to describe how we got here, your word of first choice would not be rational.