Donald Tusk’s clear rejection of Theresa May’s Chequers plan at the Salzburg summit yesterday should not come as a surprise. The most important lesson of the Brexit negotiation is that it is not a negotiation, and never has been. Blessed with superior size, wealth and power, the EU has been able to dictate the framework and substance of the talks, and has refused any deviation from its red lines.

The second most important lesson of the Brexit negotiation is that the EU will prioritise its economic and political cohesion above all else. That cohesion rests on two key outcomes: an undivided single market and an open border on the island of Ireland.

It is these principles that have led us to Salzburg. The EU will not accept the Chequers plan, which proposes a single market in goods but not in services, capital or people. It will also not accept any possibility of border infrastructure in Ireland, which is anathema to Dublin and, according to the Police Service of Northern Ireland, presents a credible risk of sectarian violence. That has duly paved the way for the Brexit endgame, which EU negotiator Michel Barnier has now confirmed: there will be a border for goods in the Irish Sea.

Brexit: May humiliated by Salzburg ambush as she fights to save Chequers Read more

The EU does not, however, want to antagonise or humiliate the UK, and has scrambled to defuse the drama of this development. Barnier stresses that most checks between Britain and Northern Ireland will take place in offices and warehouses, and only live animals and food products will need to be examined at ports themselves. But no amount of diplomatic politesse can conceal Brexit’s reality: one part of the UK will be economically split from another.

Theresa May effectively guaranteed this impasse last December, when she agreed the Irish backstop. The backstop guarantees, as a last resort, Northern Ireland’s alignment with Ireland on the customs union and single market to ensure the free flow of goods. Northern Ireland would be permitted to retain the single market just in goods because the Good Friday agreement depends on it. But no such exemptions would ever be open to the rest of the UK. Although the EU was too coy to admit it at the time, this always meant that the whole UK would have to commit to the prospect of staying in the full single market and customs union, or else concede the erection of trade barriers within its territory.

If May had been armed with political judgment, or merely cognisant of reality, she would have prepared the British people – and government – for that concession. She has instead wasted nine months denying she ever made it. It comes as little surprise that the EU has now taken the initiative where the UK refused.

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The prime minister has boxed herself in with promises she cannot keep. She insists on the ability to strike UK-only trade deals and end free movement of people, while refusing to accept its consequences. In Salzburg she announced “the idea that I should assent to the legal separation of the United Kingdom into two customs territories is not credible”, but failed to acknowledge the lack of credibility in any other option. She resembles a desperate fugitive who urgently needs to escape a building but instead keeps inexplicably locking herself inside it.

The most problematic consequence of the EU’s proposals is one that Brussels is most loath to spell out. This is not simply about checking goods. If Northern Ireland permanently operates a different customs regime from the rest of the UK and implements EU tariffs, then Northern Ireland must be exempt from any future UK trade deals. But it is almost inconceivable that the DUP – let alone the UK parliament – would ever agree to such a scenario. The DUP leader in the Commons, Nigel Dodds, has referred even to the checking of goods as “separating Northern Ireland from Great Britain”.

Quick guide Will the Chequers agreement survive? Show Hide Who dislikes the Chequers agreement and why? Noisiest in their opposition are Tory Brexiters, not least David Davis and Boris Johnson, both of whom quit the cabinet in protest. They argue that the promise to maintain a common rulebook for goods and other continued alignment will mean a post-Brexit UK is tied to the EU without having a say on future rules, rather than being a free-trading independent nation. Labour has also disparaged the proposal, expressing deep scepticism about the so-called facilitated customs arrangement system. What about the EU? Brussels has sought to stay positive, but has deep concerns about elements of the plan viewed as overly pick-and-mix, and thus potentially incompatible with EU principles. Michel Barnier, the EU’s chief Brexit negotiator, says he opposes both the customs plan and the idea of alignment for goods. He also makes plain his contention that the Chequers plan contains no workable idea for the Ireland-Northern Ireland border. But at the same time the EU has been careful to not entirely dismiss the proposals, raising the possibility it could accept some adapted version. Who supports the agreement? Officially, May and her cabinet, though even here the backing can seem lukewarm at times. Asked about Chequers, the home secretary, Sajid Javid, said it was the government’s plan “right now”, indicating alternative ideas could be considered. Is it doomed? Even May’s allies concede it will be a hugely difficult task to get the plan through parliament. Damian Green, the PM’s close friend and former de fact deputy, described the process as “walking a narrow path with people chucking rocks at us from both sides”. On the remain side of the Conservatives, the former education secretary Justine Greening called the Chequers plan “more unpopular than the poll tax”, saying May should start again from scratch. If anything can save the plan – and it’s an outside shot – it will be a combination of the hugely tight timetable and the fact that, as yet, no one else has yet produced a plan with a better chance of being accepted by parliament. What happens next? On 20 September, an informal gathering in Salzburg, Austria, will provide a snapshot of current EU thinking. Then, 10 days later, the Conservative conference could show the Chequers plan is holed below the waterline. If it survives these tests, the proposals will then reach the crucial EU summit Brussels on 18 October, with something final needed, at the very latest, in the next two months. PETER WALKER

May consequently has two tasks. First, she must determine whether her government would survive opposition to an effective border in the Irish Sea from the DUP and Commons. But more important, she must decide whether she values the economic integrity of the UK more than the ability to unilaterally change Britain’s tariffs and end migration rights for Polish plumbers.

The EU, for its part, knows it holds all the cards and recognises the danger of giving ground. Its priority is to accommodate Dublin, not London. It also concludes that a government so determined to leave must believe it can look after itself. Brussels has no reason or incentive to make any better offer.

The government has never understood the Brexit process and therefore has always botched it. It expects the EU to treat the UK both as an equally powerful third country, and as a member state still deserving the EU’s protection. It is neither. And so in a battle of red lines, the UK will lose. That is the most brutal lesson of all.

• Jonathan Lis is deputy director of the thinktank British Influence