Last weekend British and EU negotiators grappled desperately yet again with trying to find a solution to the conundrum of the Northern Ireland border. They failed yet again. That is because there is no solution, at least not one that is acceptable to the coalition that keeps Theresa May in power.

As the Northern Ireland Affairs Committee report states: “We have seen no evidence to suggest that, right now, an invisible border is possible.” It went on to conclude that, despite scouring the world for examples, they could find no technical solution that would remove the need for physical infrastructure at the border.

Theresa May’s latest Brexit speech failed even to try and suggest a practical way forward. Jeremy Hunt let the cat out of the bag unintentionally as to why, when he said the Prime Minister’s speech had achieved its real objective by uniting the warring wings of the Tory party. The Government has been negotiating with itself for the past two years rather than paying attention to the position and interests of its negotiating partner. Whether this is from wilful ignorance of European attitudes or the all-consuming importance of maintaining the uneasy coalition that keeps Theresa May in power is hard to say.

But the Government needs to distinguish between what the Chancellor dismissed as the EU’s “negotiating strategy” and its bottom line if it is going to make progress. I am certain the UK can negotiate up from the “Canada Dry” free trade deal the EU will put to us. But the EU will not agree to May’s proposal that we enjoy the benefits of the single market in the areas we choose without taking on the obligations it requires. The difference between the two is fundamental.

The issue on which this mismatch of intentions is going to come to grief is the Northern Ireland border. Theresa May made a series of contradictory promises in the December agreement with the EU. She promised the Irish no hard border; she promised the DUP no border in the Irish Sea; she promised the Brexiteers we would leave the single market and the customs union; and she promised the EU there would be full regulatory alignment between North and South for matters relating to “the all-island economy”.

To square this circle she put forward three possible answers: that the issue could be solved by technology; that the free trade agreement with the EU would be so good that there would be no need for a hard border anywhere, let alone Northern Ireland; or, if neither of these worked, that the full alignment with the rules of the internal market and customs union would be maintained.

David Davis can 'live with' a shorter transition period than the UK wanted

In its draft of the legal divorce agreement, the EU had no choice but to include language on the third, fallback option alone. Even after two years there have been no practical proposals for the first two, so there is nothing on which to base a legal draft. The Government and the DUP feigned high dudgeon. But all the text did was render in legal language what they had agreed politically in December. The EU could, I suppose, have drafted it to leave the whole of the UK in the customs union and the single market rather than just Northern Ireland, but it is not obvious that would have been any more welcome to the Brexiteers.

There is of course a reason why the British Government has not put forward practical proposals for the first two options, despite having nearly two years in which to do so. It is because neither option can or will avoid a hard border.

The technological solution is dismissed by the EU as “magical thinking”. An Irish Revenue study leaked last year made it clear that a hard border could not be avoided by technological means. The Brexiteers have been pinning their hopes on a paper by Lars Karlsson, a former employee of the World Customs Organisation, one of a number presented to a committee of the European Parliament. I assume that is because they have not read it. The technology he proposes is untested and by his own admission would take years to roll out. The paper does not consider the regulatory, as opposed to customs, requirements which mean there would need to be checks. And in any case his plan involves physical infrastructure, including gates, on the border.

Theresa May suggested that small business should be exempted from border checks and that would remove most of the problem. She perhaps forgets that Slab Murphy is a small businessman and that smuggling has been rife on this border for a century. Even if the UK didn’t insist on a hard border, the EU would have to do so to prevent a gaping back door into the single market. She recently proposed the US/Canada frontier as a model but, as someone who has repeatedly crossed between the two countries, it certainly looks and feels like a hard border.

In any case the principal problem is not the time it takes a lorry to pass the border but the impact a hard border is going to have on the peace process. The Good Friday Agreement was all about identity. People in Northern Ireland could feel British, Irish or both because there is no visible border. Once we again block off the small back roads with huge concrete slabs to stop smuggling and put in checkpoints on the main roads, we reopen the issue of identity. That does not mean we are automatically tipped back into the Troubles (although as the chief constable in Northern Ireland points out the checkpoints will be targets for dissident terrorists) but it does mean we force Northern Ireland back into identity politics. It will become even harder to restore the executive than it has been over the past year, during which time the province has languished without a government.

The other solution the Government has offered is a new type of trading relationship between the EU and the UK as a whole that would avoid hard borders anywhere. This is essentially the idea that we could opt into the single market for the trading areas we like and opt out of the rest, including the obligations to pay, accept free movement and jurisdiction of the ECJ. Not surprisingly, the EU negotiating guidelines make clear the free trade agreement “cannot offer the same benefits as membership and cannot amount to participation in the single market or parts thereof”. And that is not their “negotiating strategy”, that is what they mean.

What the Government fail to recognise is that there is not a continuum between a Canada-style free trade agreement and Norway-style participation in the single market where you can choose David Davis’s “Canada plus, plus, plus” agreement (by which he means getting the benefits of the single market). They are completely different animals.

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Since the Government has decided to take us out of the single market and the customs union, we are going to end up with a variant of the Canada-style free trade agreement. If we negotiate skilfully it may be on better terms than the Canadians secured, but it is still going to be a free trade agreement. As Theresa May acknowledged in her speech, a Canada-style agreement will “mean customs and regulatory checks at the border” and will therefore be “inconsistent with the commitments both we and the EU have made in respect of Northern Ireland”.

And, by the way, the Labour solution of a customs union doesn’t solve the problem for Northern Ireland either. The EU draft divorce treaty makes it clear the province would effectively need to be in the single market as well as the customs union to avoid regulatory differences, particularly in the agricultural sector, which would otherwise require border checks. The arch Brexiteer Jacob Rees-Mogg has, in desperation, suggested that we should demand that Ireland leave the customs union and the single market so we can resolve the problem.

Theresa May has therefore committed the worst possible sin a negotiator can commit. She has boxed herself in. She may hope that she can again fudge the issue, by pretending the border is soft rather than hard. But the fudge doesn’t work anymore. The Government will have to agree the legal text of a divorce treaty in October if we are to leave by March next year. And legal texts are not susceptible to constructive ambiguity. She will be faced by the alternative of accepting the current EU draft and losing the support of the 10 DUP MPs who sustain her Government or alternatively accepting that the whole of the UK remains in the single market and the customs union in which case she will lose the support of the 62 backbench Brexit Tories.

She may hope she can instead persuade the EU and the Irish government to delay the issue for further negotiation during the two-year transition rather than decide the issue in October. But so far, the Irish have been adamant the border be resolved now while they still have leverage, and the rest of the EU has stood with them. Donald Tusk reiterated in Dublin that it would be “Ireland First”. It would be a colossal gamble for the Government to stake everything on being able to break that united front at the last moment. And if they don’t, we risk crashing out of the EU without an agreement at all.

Theresa May’s speech may have temporarily united the Tory party, but it has not solved the substantive problems. Indeed, her problems on Brexit may only just have begun and it may turn out that the insoluble problem of the Northern Ireland border is the issue that finally brings the entire negotiation crashing down.