Theresa May’s early visit to Donald Trump probably seemed like a good idea at the time. Pushing to the front of the White House queue is what British prime ministers do when there’s a new US president. Trump knows and likes Britain too, to the extent that he cares about any foreign country. The two countries are also allies. And new leaders need to have face time.

But the race was always a demeaning ritual, and now it is more demeaning than ever. Transatlantic relations are important, of course. But what would it matter if the British prime minister met the US president in February, rather than in January? Nothing would be lost. No other country except perhaps Israel cares so neurotically about Washington’s welcome mat.

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And anyway, this is President Trump we are talking about. It’s not Abraham Lincoln or Franklin Roosevelt. Trump is upending not just US politics but global politics too. He overturns a civilised norm every day before breakfast. He is despised in Britain, and nothing May says is going to change that.

The Washington visit is thus more fraught with dangers than opportunities for the prime minister. Even her senior supporters say they are struggling to think of the positives. They, and probably she, will likely be content if she gets back without anything too disastrous having happened.

There is an immediate danger with the visit and an underlying one. Both are large. The immediate one is Trump himself. What he is doing on issues such as torture, wall-building, China or entry bans is reckless enough. But what he might say with May by his side is the stuff of spin doctors’ nightmares. She doesn’t do personal chemistry, and he is loathsome.

May is not stupid. Nor are those advising her. To put it mildly, they know there are pros and cons. Before the election they could be scathing about Trump and his people. But they have decided, rationally enough, that they still need a serious relationship, even with Trump. They are right. It has to be done, if only to coordinate intelligence and to help pull Trump back from policies that could abandon eastern Europe to Vladimir Putin.

But not at absolutely any price. May will lose credibility at home if she does not put clear distance between herself and some of the things Trump has been saying. Above all, rejection of torture should be a red line, both on principle and in practice – but also because, as Tony Blair found, a reputation can unravel if one equivocates. May must beware the perils of poodledom.

May needs to make time in Washington to denounce torture. This feels even more raw to me this week because of Wednesday’s untimely death of Nigel Rodley – the longtime legal chief of Amnesty International, a former UN rapporteur on torture and a lovely and principled man. His memory demands a clear and immediate statement against torture from our prime minister.

But the deeper and underlying danger is this. The US-UK special relationship remains far more important to the British governing class than it does to the Americans. It too often skews British thinking. That was true even in the cold war, and in the aftermath of 9/11. Even Margaret Thatcher and Tony Blair struggled to make it convincing. But with an “America first” president, it risks seeming more delusional than ever.

All this is spiced up by Brexit, as is everything in British politics now. Brexit means London’s wish to be embraced in Washington has been heightened, because our back is turned on Europe, because we are a trading nation, and because the world remains a dangerous place. A trade deal with the US is top of the leavers’ wish list, but this too is a potentially treacherous prospect. It owes more to the wishful thinking of UK Atlanticists than to hard economic reason, which still points firmly to Europe.

Brexit’s impact has hustled May into this visit in other ways. Don’t underestimate the Farage factor. The former Ukip leader’s closeness to Trump may be a bid of a fraud on both sides, but it has freaked out both No 10 and the Foreign Office. Boris Johnson’s recent trip, and now May’s, have been accelerated by the need to push Nigel Farage firmly to the margins. May’s priority of priorities is to squeeze the air out of the Ukip threat.

Trying to understand Trump better is important. May needs to do it. We all need to do it. Indignation and outrage are necessary, but not enough. But there is no need, either in principle or in practical statecraft, for kowtowing before Trump’s chariot.

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As she heads for Washington, May is on the threshold of making her own version of Blair’s error. In 2001 at Camp David, it was not wrong for Blair to be chummy with George W Bush. That was necessary statecraft, especially for someone who had been so close to Bill Clinton. The error was to imagine that British public opinion didn’t want him to do anything else.

Blair always exaggerated the extent to which the mood of British politics was downstream from that of America. It led him not just to misread Bush but to misread the British view of Bush, in the end disastrously.

In today’s different circumstances, May is herself treading very close to the edge. The British dislike Trump. They want him to stop disrespecting Nato and international norms. They will soon learn that the US approach to trade is “the American way or no way”, especially now.

To talk, as May does, about the Brexiting UK and Trump’s US “leading together again” is the language of pure folly. It is a reminder of how much damage Brexit is doing to the national interest. And she shouldn’t make it worse. If May thinks that waving a piece of paper signed by Trump offering a US trade deal will be viewed as a triumph, she is wrong. It could make her not the new Margaret Thatcher, but the new Neville Chamberlain.