Perhaps it’s all part of a cunning plan. Maybe there’s a secret strategy document stashed in a Downing Street vault, codenamed Operation Wind-up. The classified text will reveal that the UK government’s negotiating tactic is to drive our fellow Europeans mad, to infuriate them through so many contradictions, contortions of logic and outright violations of previous agreements that they’ll end up reduced to a sobbing, gibbering mess, ready to concede to Theresa May whatever she wants, just to make the madness stop.

Theresa May 'will refuse Brexit deal that threatens UK integrity' Read more

How else to explain the way London is approaching the Brexit talks with the remaining 27 states of the European Union? The latest double attempt to goad the Brussels negotiators into tearing out clumps of their own hair comes from Boris Johnson. On Tuesday, he managed a full-spectrum insult when he suggested that the border between Northern Ireland and the Irish republic was of no greater significance than the boundary that separates the London boroughs of Camden and Westminster. In its ability to offend multiple groups at the same time, it was almost brilliant. It simultaneously disrespected Ireland’s status as a sovereign nation, trivialised a conflict that cost thousands of lives, downplayed an issue which matters enormously to the European Union – and all with a London-centric focus that screamed metropolitan elite. Not bad for a single sentence in a radio interview.

Play Video 0:35 'Like the congestion charge': Boris Johnson on Irish border checks post-Brexit – video

Overnight, he’s dialled it up a notch, thanks to the leak to Sky News of a letter Johnson wrote to May suggesting the way the government can solve its Irish border problem is by reneging on the agreement May made with the EU in December. Back then the prime minister solemnly vowed that there would be no hard border on the island of Ireland. In his letter, Johnson tells May that there could be some wiggle room, since all Britain promised was to “stop this border becoming significantly harder”. (That word “significantly” offers plenty of leeway.) He goes further, explicitly countenancing the reintroduction of a hard border since less than 5% of goods would require checks.

You’d forgive Michel Barnier and his team finding the nearest wall and banging their heads repeatedly against it

You’d forgive Michel Barnier and his team finding the nearest wall and banging their heads repeatedly against it. They thought everyone had understood and agreed on this point: no hard border means nothing tangible or visible that could become a symbol and target for republican paramilitaries, whether used to check 1% or 100% of goods. Yet here is the British foreign secretary either being obtuse or else wilfully urging the prime minister to break her word.

But Operation Wind-up does not rely on Johnson alone. Former Brexit minister David Jones did his bit this morning, telling BBC Radio 4’s Today programme that if Northern Ireland ends up remaining in the customs union and single market – as envisaged in the “backstop” scenario, outlined in the draft text of the withdrawal agreement published in Brussels today – then that would amount to “annexure” (he meant annexation) of Northern Ireland by the EU. Without going full Basil Fawlty, Jones was deploying the hoary trope of an aggressive, expansionist EU posing a 1940s-style threat to a defiant United Kingdom.

No less maddening was Jones’s dismissal of today’s EU legal text as an “opening salvo” in negotiations. No: it’s a formal account of an agreement that was reached back in December, following so-called phase one negotiations. The UK might want to tweak the wording, but the fundamentals have been agreed by May and the EU. That phase one stage of talks is not “opening”, it’s closed.

EU publishes plan to keep Northern Ireland in customs union Read more

Of course, all these little irritations arise from the big one, which is the Brexiteers’ refusal to see that they are asking for a series of things that are mutually incompatible. They want Britain out of the single market and customs union. They want no EU/UK border in the Irish Sea that would distinguish Northern Ireland from Britain. And they say they want no hard border in Ireland. You can have one or two of those, but not all three. (My long-held suspicion, confirmed by the Johnson letter, is that if something has to give, the Brexiteers’ first instinct would be to sacrifice Ireland.)

The Europeans know that, and are imploring Britain to recognise it too. No amount of magical thinking can wish it away. Jeremy Corbyn acknowledged as much on Monday, with his shift on the customs union. But the Brexiteers pretend this circle can be squared, if only the Europeans would close their eyes tight and believe. Instead, the government is driving our partners to distraction, souring the atmosphere for the next phase of negotiations when goodwill will be an essential commodity. All this might be driving Brussels to bang its collective skull on the desk – but it’ll be Britain that gets the headache.

• Jonathan Freedland is a Guardian columnist