Donald Tusk, the president of the European council, described the problem of the Irish border after Brexit as the Gordian knot of the negotiations. Alexander the Great solved the problem of unpicking a tightly woven rope by slicing it in half. In Brussels and Whitehall, the plan appears to be to add more tangles as if to make the original knot disappear.

The knot

The UK committed last December and in March to the inclusion of an “all-weather” protocol in the withdrawal agreement that would ensure a hard border on the island of Ireland would never return under any circumstances.

Quick Guide Brexit and backstops: an explainer Show A backstop is required to ensure there is no hard border in Ireland if a comprehensive free trade deal cannot be signed before the end of 2020. Theresa May has proposed to the EU that the whole of the UK would remain in the customs union after Brexit, but Brussels has said it needs more time to evaluate the proposal. As a result, the EU insists on having its own backstop - the backstop to the backstop - which would mean Northern Ireland would remain in the single market and customs union in the absence of a free trade deal, prompting fierce objections from Conservative hard Brexiters and the DUP, which props up her government. That prompted May to propose a country-wide alternative in which the whole of the UK would remain in parts of the customs union after Brexit. “The EU still requires a ‘backstop to the backstop’ – effectively an insurance policy for the insurance policy. And they want this to be the Northern Ireland-only solution that they had previously proposed,” May told MPs. Raising the stakes, the prime minister said the EU’s insistence amounted to a threat to the constitution of the UK: “We have been clear that we cannot agree to anything that threatens the integrity of our United Kingdom,” she added.

The EU proposed that Northern Ireland should in effect stay in the single market and the customs union as the UK withdrew at the end of the 21-month transition period, unless there was some great trade deal or bespoke solution that could ensure there was no need for border checks.

Theresa May rejected it. She said no British prime minister, and certainly not the Democratic Unionist party on which May’s government depends in the Commons, could tolerate the prospect of Northern Ireland being in a different customs territory to the rest of the UK. That would require a border being drawn in the Irish Sea, and a different set of tariffs being applied on imports to Northern Ireland than those to Britain.

The government responded that under the backstop the UK as a whole would stay in the shared customs territory on a time-limited basis.

The response from Brussels amounted to interest in a UK-wide customs union with the EU, but a refusal to countenance it as a replacement in the withdrawal agreement for the text specific to Northern Ireland.

A backstop proposal could not be time limited as it would not be a backstop, and an all-UK customs union would require lengthy negotiation over its terms to ensure British companies did not enjoy a competitive advantage as the UK law book diverged from the EU’s.

There was also some querying of the government’s intentions about the single market aspect of the backstop, by way of EU standards. Under the EU’s plan new regulatory checks would emerge on goods flowing across the Irish Sea as Northern Ireland remained under Brussels regulations while the rest of the UK exited.

Extra tangle number one

In terms of the single market, Downing Street appears to accept that Northern Ireland might stay under EU regulations as Britain diverges. It would just be a matter of scaling up checks on agricultural imports, and the impact of checks on standards on goods could be lessened by them being made away from the Irish Sea border, in factories or in the market place.

It also appears, however, that in order to maintain Northern Ireland’s untrammelled access to the UK market, Downing Street might dispense with checks going from west to east across the Irish Sea, even though they would be in force on goods going the other way.

Extra tangle number two

In terms of customs, an outline of what may be happening could be seen in the prime minister’s statement to the Commons on Monday. May said she would not accept a customs border in the Irish Sea. She then told MPs “we must make the commitment to a temporary UK-EU joint customs territory legally binding so the Northern Ireland-only proposal is no longer needed”.

Downing Street may be briefing something different at this stage, but May’s words do not amount to an insistence that the EU’s proposal should disappear from the legal text. She appears to be seeking a legal obligation on the EU to devise a UK-wide deal that would make the toxic Brussels proposal superfluous. The UK is also open to extending the transition period to allow that specific negotiation to come to fruition.

In Brussels, meanwhile, all mention from the original EU backstop of a customs territory is being scrubbed from the withdrawal agreement, to be replaced with arcane references to regulation No 952/2013, which deals with the rules of the EU’s customs territory that would apply to Northern Ireland.

The original knot is vanishing before our eyes.