Winston Churchill once wrote that the balances of world history can sometimes turn on what he called “small agate points”. Churchill had in mind the accidental shooting of the American civil war general Stonewall Jackson by his own men in 1863, without which, he speculated, the Confederate armies might have captured Washington DC, and the United States might have split into two. But he could have been talking of Donald Trump’s latest tweets and their implications for British foreign policy after Brexit.

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Trump’s overnight tweet is at once both trivial and epochal. “@Theresa_May, don’t focus on me,” Trump tweeted in the small hours. “Focus on the destructive Radical Islamic Terrorism that is taking place within the United Kingdom. We are doing just fine!” On one level this was just another piece of late-night, extremist presidential scattergun. But on another it was a high-velocity bullet aimed unerringly at the cerebral cortex of the UK government’s international strategy.

Trump sent a variety of messages in those 26 words, all of them foul. At their root is the anti-Islamic prejudice that the president routinely fosters among his extreme-right political base. He may not have cared much that the source of the anti-Islamic videos that he shared on Twitter on Wednesday was a tiny and virulent British extremist group, Britain First. But he certainly cared that the videos had been promoted by the motormouth US rightwing propagandist Ann Coulter, one of his key advocates. And he will have felt vindicated not embarrassed by the response on the far right. “Thank God for Trump! That’s why we love him,” tweeted the former Ku Klux Klan leader David Duke after Trump shared the hate videos.

Do not forget, either, that an America First president is naturally sending his tweets to Americans first. This week he is seeking to rev up support for his wall-building plan on the US-Mexico border. Trump has recklessly made funding for the wall a condition for a budget deal with Congress. He is under pressure to deliver a victory to his far-right supporters, not least because he has so far failed to abolish Barack Obama’s affordable healthcare legislation.

But the budget stand-off – already the third of his presidency – is not going well. Mexicans are not Muslims, but attacking Muslims is intended to turn up the heat on Congress over America’s principal source of illegal migration. The paradox is that Trump’s actions seem increasingly likely to hand a victory in Mexico’s 2018 presidential election to the anti-Trump leftwing candidate Andrés Manuel López Obrador, widely known as Amlo, rather than boost the chances of Trump’s own domestic vanity project.

But the Trump Twitter-storm aims a wrecking ball at Theresa May too. During the course of the year, May has tried hard to avoid becoming embroiled in global disapproval of Trump. But even she has been forced to distance the UK from some of the president’s most important international disruptions, notably his travel ban, and his stances on climate change and Iran. Until now, though, the language of difference has been relatively nuanced and diplomatic, with the UK siding with the international rules-based order against Trump’s unilateralism.

This is different because it is more direct. It is a direct challenge to Britain and its values. May could not avoid commenting on Trump’s retweeting of the Britain First videos while at the same time credibly maintaining her own genuine commitment to anti-racism. But now the argument has also become personal. For an American president to address a British prime minister in this manner and on such a subject is without any modern precedent. It draws a line about values. May and Trump are on different sides of it. Trump is not May’s friend, Britain’s friend or a friend of the values that this part of the world stands for and must uphold.

Britain should ask for an apology. In a rare – much too rare – intervention in UK politics on Thursday, David Miliband called Trump’s tweets “dangerous, irresponsible, hateful, jaw-dropping, offensive to everything we should stand for” and suggested an apology was due. And so it is. May should reprimand Trump publicly and on the record.

The tweets also make a Trump state visit to Britain inconceivable, now or at any other time. The original invitation was wholly premature and inappropriate. Even a few months ago it was clear that any Trump visit would trigger levels of protest that would destroy whatever dubious value the idea might have possessed in the first place. Now the case is far feebler than before. To allow a Trump visit now would be an endorsement of his racism. London will probably prefer to let the matter disappear. But the principled course would be to withdraw the invitation altogether.

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All this is important and difficult stuff. Yet it is overshadowed by two much larger issues for Britain. The first is the damage to the so-called special relationship. Trump has not yet destroyed the importance of the north Atlantic alliance to Britain, but he unquestionably makes it more difficult to uphold and defend in anything approaching the traditional way. With the idea of common values between Britain and Trump’s America now so threadbare and threatened, the special relationship, which was never as deeply embraced in America as it was in Whitehall, now looks not just delusional but morally compromised.

Every other major European nation has been more honest and practical about facing up to this than Britain. May blundered into a premature and personally discreditable early visit to Trump, whereas Angela Merkel kept her distance and Emmanuel Macron tried a charm offensive on Gallic terms. The real questions for the north Atlantic partnership are which parts can be resiliently maintained while Trump remains in office, and what happens post-Trump. Both of these require honest not naive answers.

The realities of Trump and the uncertainty about what comes afterwards also aim a dagger at the Tory party’s post-Brexit delusion about global Britain, particularly the white Anglosphere incarnation beloved of the fiercest Brexiters. Every reality facing May – economic, political, cultural and strategic – screams that the closest practicable relationship with the EU is Britain’s proper and principled destiny. Brexit was always a disastrous course for Britain. Trump’s tweet should be one of those small agate points that turns the balances of the world, just as Churchill said.

• Martin Kettle is a Guardian columnist