HOW Theresa May must wish she'd never let Donald Trump hold her by the hand in the White House garden last year. That image cannot be erased. Nor can the extraordinary diplomatic exchanges last week between Britain and the US over the President's retweets of racist propaganda. It seems no-one told The Donald that America's “special relationship” wasn't meant to be with Britain First.

Some in the UK Government were probably rather relieved because the Twitter spat diverted attention from the troubled state of the Brexit negotiations. But the episode surely confirms the naïveté of believing that Britain could walk out of the EU and into a preferential, bells-and-whistles free trade agreement with the US. Not under a president as irrational and self-interested as Donald Trump. It just ain't gonna happen.

Perhaps this belated realisation explains why the British Government pretty much gave up in the Brexit negotiations last week. On the three key issues of money, Ireland and citizens' rights, the UK has essentially agreed to the terms of the Brussels negotiator, Michel Barnier, set out at the very start of this process back in September. After all the bluster, the belligerence and the posturing, the UK has thrown its hands in the air and said: OK, whatever.

Last week's capitulation on the 50 billion euro divorce bill was the most humiliating U-turn so far. As recently as last April, the Foreign Secretary, Boris Johnson, was telling Brussels to “go whistle” for its “extortionate” demands. A House of Lords committee opined that Britain didn't owe the EU a penny. Brexiteer MPs, like John Redwood, said Britain would stand firm against “intimidation”.

Well, so much for all that. It's clear that the UK will be paying at least 50 billion, and possibly a lot more depending on the terms of the transitional trade arrangements. No-one knows for sure what the final figure will be. The BBC reported last week that Britain may still be paying to Brussels for another 30 years, until an entire generation of EU bureaucrats retires.

To hide its embarrassment, the Government is now suggesting that none of this really matters: that 50 billion is a drop in the bucket, a small price to pay etc. But the mystery is how Theresa May ever persuaded herself that the result would be any different. There was never the remotest chance of Britain getting out of its EU obligations scot-free. From the rigid timing of Article 50 to the sequencing of trade talks, Britain was always in a weak bargaining position. We always had more to lose from a no-deal Brexit than Europe did. Britain was holding a gun to its own head and threatening to pull the trigger if Brussels didn't relent.

It’s best to avoid gun metaphors as far as Northern Ireland is concerned. The impact of Brexit on the peace process was always high on Brussels's agenda, but the UK made the mistake of believing that this was disingenuous, and that Barnier had only raised the Irish border issue in order to extract more money from Britain. It wasn't. The EU was only stating the obvious: namely that if the UK leaves the EU Customs Union there will be a land border in Ireland. By definition this means customs and excise posts, regulatory issues and immigration controls.

Desperate to get trade talks started at the crucial EU Council next week, UK sources briefed the London Times to the effect that there had been a “breakthrough” on the issue. The paper claimed that the UK Government had agreed in principle that there would be no “regulatory divergence” on crucial matters like agriculture in future between Northern Ireland and the Republic after Brexit. The sources insisted that this did not mean that Northern Ireland was remaining in the EU single market, or that there would be a new border on the Irish sea.

Understandably, Dublin is sceptical about this vague proposal. Their Foreign Minister, Simon Coveney has demanded an agreement, in writing, that Northern Ireland will retain the same regulatory environment as the rest of the EU after Brexit – not just on agriculture, but for medical matters, drugs, food safety, animal welfare and a host of other things. Most of Ireland's exports go through the UK via the North, and the Dail is understandably worried that a hard border will impede that trade. They also worry about border posts, however discreet, becoming a target for paramilitary groups.

The British seem adamant that they can give these assurances without Northern Ireland remaining in the single market. But Democratic Unionist Party MPs, upon whom Theresa May depends for her majority in Westminster, smell a rat. “If this is about leaving Northern Ireland half in the EU,” said the DUP MP Sammy Wilson,”it's not on”. The DUP leader, Arlene Foster has said she “will not countenance any new border in the Irish Sea”. But it's very hard to see how the UK Government proposal can avoid this. The border has to go somewhere.

Theresa May has clearly decided to allow Ulster to retain some form of continuing relationship with the EU. It is perhaps one of those anomalous “special arrangements” that were rejected for Scotland. Last December, the Scottish Government”s White Paper, Scotland's Place In Europe, proposed a number of options, including the so-called “reverse Greenland” whereby Scotland could remain partially in the EU single market while the rest of Britain left it. Theresa May insisted that such an arrangement was out of the question because “the UK is leaving the EU as one country” and there could be no fuzzy edges. Brexit means Brexit. One out; all out.

This would appear no longer to be the case vis a vis Northern Ireland. But before the Scottish Government leaps up to declare #metoo, it would be wise to wait until the detail of this proposal emerges this week. It's not at all clear it’ll happen. Irish newspapers are livid at the attitude of Britain to the border issue, and all the main Irish parties support the Taoiseach, Leo Varadkar’s, threat to veto the Brexit negotiations if they don’t get regulatory convergence.

The third Brussels demand, that EU citizens remain under EU law after Brexit, has already been largely conceded by the Exit Secretary David Davis. With all this it’s a fair bet that many British voters are having second thoughts about Brexit. So, is it time to call for that second EU referendum, and give British voters an “exit for Brexit” as the LibDem leader, Vince Cable, puts it? Probably not.

Most Leave voters weren't really interested in trade, but in immigration. The other big news of the week is that inward migration to Britain has fallen by over 100,000 – one of the biggest drops ever recorded. This should be no cause for rejoicing because it is mostly skilled and industrious EU workers who are returning. Their loss will not be our gain. But to Leavers it looks as if Brexit is doing exactly what they hoped it would do: send immigrants back home. The British economy may be tanking, but if there were another referendum tomorrow, the result might not be very different from 2016.