Like Elvis meeting Nixon, the president-elect and Nigel Farage grin, thumbs up, in the gilded vulgarian’s paradise of Trump Tower. This image is a reward as sweet as any the interim Ukip leader might have hoped for – sweeter, perhaps, than the EU referendum result itself. It adds bludgeoning force to his claim to be our man in the new Washington, in practice if not by official appointment.

As for Trump: could there be clearer evidence that the next leader of the free world lacks all sense of decorum and diplomatic protocol? On Thursday he schmoozed the prime minister, Theresa May, in a telephone call, the warmth of which delighted (and relieved) her officials. There is a guarded hope among her allies that she might gently steer the 45th president towards a more realistic position on free trade, Nato and the containment of Russia.

In his conversation with the PM, Trump cited the precedent of Ronald Reagan’s relationship with Margaret Thatcher. A more productive inspiration would be Macmillan’s bond with Kennedy. In a memo disclosed in the Sunday Times, Sir Kim Darroch, the UK’s ambassador in Washington, expressed the hope that the president-elect would be “open to outside influence if pitched right … we should be well placed to do this”.

I understand that in an unpublished section of Trump’s call to May he signalled that his campaign rhetoric should not be taken too literally. It is understandable that the PM welcomed this – who would not? – and that the government hopes to steer the president-elect towards some version of sanity.

But May’s team should manage their expectations. One cannot assume from Dr Jekyll’s occasional appearance that Mr Hyde is gone for good.

Still, how strong is the yearning to believe that Trump is something other than what he patently is – that office will soften him and smooth his rough edges, that he will be tamed by the presidency. Let us call it Von Papen syndrome.

Farage meets Trump: ‘This image is a reward as sweet as any the interim Ukip leader might have hoped for.’ Photograph: ‏@Nigel_Farage/twitter

In 1933 the German vice-chancellor, Franz von Papen, looked forward to “boxing Hitler in”, and claimed: “Within two months we will have pushed Hitler so far in the corner that he’ll squeak.” These boasts were, to put it mildly, mistaken (but just to anticipate seething Trumpist trolls: I am drawing an analogy, not suggesting direct equivalence between the Führer and their American hero).

Here there is a strong parallel with the debate on Britain’s departure from the EU. Just as some politicians imagine that there can be a “soft Brexit”, so the delusion has arisen that the “hard Trumpism” of the campaign will yield place to a soft Trumpism in office. Yet consider how the president-elect responded when the Wall Street Journal asked him whether he had gone too far. “No,” he replied. “I won.” This is scarcely the voice of humility.

The new special relationship, in any case, is not between leaders or governments. It is a malignant cultural tendril that stretches across the Atlantic connecting Brexit to Trump’s election and all it portends. This is what really matters.

The symmetry is not exact. In practice, the “left behind” played a greater part in the referendum result than in the presidential contest: about two-thirds of those with incomes under £20,000 voted to leave the EU. In contrast, a higher percentage of low-income voters opted for Hillary Clinton than for her Republican conqueror.

Richard Nixon meets with Elvis Presley at the White House in 1970. Photograph: White House/AP

Trump, furthermore, faces few institutional constraints: his party controls both Congress and Senate, and he has pledged to mould the supreme court in his image. How the Brexiteers must envy him, as they reel from the high court’s decision that parliament must give its approval to the triggering of article 50.

Yet in spite of these differences it would be idle to deny the pulsing connection between the two movements. Both Brexit and Trump’s election have conspicuously released the toxins of racism, xenophobia and homophobia.

According to the National Police Chiefs’ Council, the number of hate crimes rose by 58% in the week after the vote to leave the EU. In July, August and September, homophobic incidents increased by 147% compared with the same period last year.

In the US a similar pattern is asserting itself: Muslim girls are frightened to wear the hijab. The slogan “Gay families burn in hell!” appears above the hashtag Trump2016. The swastika is enjoying a revival in inner-city graffiti. In their cafeteria, Michigan middle schoolers chant “build a wall!”

These are the wages of a presidential campaign based on hatred, and one that blithely restored to the mainstream language and idiom that had been (one thought) driven out over the years by civil decency. This is Trump’s fault.

So too the Brexit movement and Trumpism share an astonishing vagueness of prescription. This is the greatest weakness of the ascendant alt-right: that loose-linked collection of digital guerrillas, pantomime acts and high-octane attention seekers.

‘Trump cited the precedent of Reagan’s relationship with Thatcher. A more productive inspiration would be Macmillan’s bond with Kennedy.’ Photograph: Bettmann Archive

They say they hate globalisation, immigration, and “political correctness”, and I dare say they do. But – like the Brexiteers and the president-elect – what they offer instead lacks detail, depth, and plausibility.

In the UK, we are allegedly “taking back control”. But how, exactly? In his meandering acceptance speech, Trump pledged to “put millions of our people to work”. Again: how? What does he know that his presidential predecessors didn’t?

For a start, the protectionism he has promised is a dead end: we know how that movie ends. As the PM will declare in a speech at the Mansion House on Monday night, the great task now is not to tear down globalisation but to make it work more equitably, not least for those “who see their jobs being outsourced and wages undercut”. This is the task of generations, not years.

What will not change – whoever is in the White House, wherever Britain stands in relation to the EU – is the intermingling, porousness and interdependence of the modern world. No wall or act of secession can halt these forces in their tracks. Nor would it make any sense to do so: the vigorous exchange of goods and labour is the greatest engine of prosperity the world has ever known. See how all those angry Trump voters like it when their smartphones cost $1,000.

Consider again that unlovely image of the president-elect and Farage: their smugness, their schoolboy brio, their confidence that common sense has at last prevailed. They believe that in their different ways they incarnate the “change” that is needed. God help them both when the voters spot the con.