There’s an unwritten rule in the EU club: national leaders help each other out at times of domestic difficulty. It might be an election, internal strife in their party or a challenge to their position.

Theresa May is trying to play this card as she meets Emmanuel Macron today at his summer retreat in the south of France. But so far, the EU has done May favours only when it was in their own interests. Last December, they agreed that sufficient progress had been made to move on to phase two of the Brexit talks, largely because they feared May would be toppled (and replaced by someone worse).

The blunt truth is that, while the UK is still technically a member of the club until next March, the special favours rule ceased to apply once May declared that “Brexit means Brexit.” The UK is already viewed as a “third country” by the rest of the EU.

That’s why the UK has failed in its attempt to “divide and rule” the EU in the negotiations. The EU27 has been impressively united; the cracks that British ministers have long predicted have not appeared. They blame the intransigence of Michel Barnier, the European Commission’s chief negotiator, but he is implementing the mandate given to him by the 27 leaders.

So May is now trying a different tack: putting pressure on national leaders to soften the line. Angela Merkel, the German chancellor, made sympathetic noises when she met May last month. May also held positive talks with Mark Rutte, the Dutch prime minister. These two meetings helped pave the way for Barnier to say yesterday the EU is “ready to improve” its plan for the Irish border question. So one-to-one diplomacy can pay dividends. May now needs Macron to engage constructively with her Chequers plan, and secure more movement by the EU.

With Merkel weakened at home, the French president is the strongest player in Team EU, but has been less sympathetic to May’s predicament than Merkel. May’s problem is that Macron will share Barnier’s hostility to her proposals on customs and for a single market in goods.

May does have a strong case for asking the EU to show more flexibility because she did that in her Chequers plan – for example, on the role of the European Court of Justice. “The EU should recognise that she showed balls and took risks,” one May ally told me. “She knew it could mean cabinet resignations and still did it. It’s time for the EU to reciprocate.”

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Although the EU may beg to differ, there is one reason why its leaders might cut May some slack. Not out of friendship, but self-interest. They didn’t need to be lectured by UK ministers about the growing risk of an accidental no-deal Brexit next March; they can see the clock ticking. The EU calculates that crashing out without a deal would harm the UK more than the bloc, but it would suffer some disruption and damage. So it wants an agreement.

However, that does not mean EU leaders will roll over and sign up to May’s Chequers plan. For many, including Macron, preserving the integrity of the single market will mean ruling out a different UK regime for goods and services – even if their own economies take a hit. The EU also has grave reservations about May’s plan for the UK to collect tariffs for goods bound for the bloc.

The problem is that, if May makes further concessions, she could face more cabinet resignations, with Penny Mordaunt, Esther McVey and Andrea Leadsom the most likely departures. There would also be more destabilisation from hardline Brexiteers on the backbenches.

So there are ominous signs that we could end up with a compromise on the Irish border, which forms part of the withdrawal agreement, and a very vague political declaration about the future UK-EU relationship, which puts off the crucial decisions on market access and customs until the implementation (or transitional) period lasting from next March to December 2020.

Such a minimalist deal might prevent a meltdown this Autumn that would bring May down. She might win over enough Tory MPs to secure Commons approval for such a threadbare deal, in order to “get Brexit over the line” next March, as Michael Gove urges. It would avoid a cliff edge exit.

It would be a good deal for the EU, which would bank the UK’s £40bn divorce payment – part of the withdrawal agreement. But it would be a bad deal for the British public. Again, Tory party management would trump the national interest. The UK will have very little leverage in the negotiations once it leaves the EU, and would have thrown away its trump card – the £40bn. It might be money for nothing, since we would have little idea about our future trade links with the EU.