For the most ardent supporters of Brexit, the election of Donald Trump was a mixture of vindication and salvation. The president of the US, no less, thinks it is a great idea for Britain to leave the EU. Even better, he seems to offer an exciting escape route. The UK can leap off the rotting raft of the EU and on to the gleaming battleship HMS Anglosphere.

It is an alluring vision. Unfortunately, it is precisely wrong. The election of Mr Trump has transformed Brexit from a risky decision into a straightforward disaster. For the past 40 years, Britain has had two central pillars to its foreign policy: membership of the EU and a “special relationship” with the US.

The decision to exit the EU leaves Britain much more dependent on the US, just at a time when America has elected an unstable president opposed to most of the central propositions on which UK foreign policy is based.

During the brief trip to Washington by Theresa May, the UK prime minister, this unpleasant truth was partly obscured by trivia and trade. Mr Trump’s decision to return the bust of Winston Churchill to the Oval Office was greeted with slavish delight by Brexiters. More substantively, the Trump administration made it clear that it is minded to do a trade deal with the UK just as soon as Britain’s EU divorce comes through.

But no sooner had Mrs May left Washington than Mr Trump caused uproar with his “Muslim ban”, affecting immigrants and refugees from seven countries. After equivocating briefly, the prime minister was forced to distance herself from her new best friend in the White House.

The refugee row underlined the extent to which Mrs May and Mr Trump have clashing visions of the world. Even when it comes to trade, the supposed basis for their new special relationship, the two leaders have very different views.

Mrs May says that she wants the UK to be the champion of global free trade. But Mr Trump is the most protectionist US president since the 1930s. This is a stark clash of visions that will be much harder to gloss over — if and when Mr Trump begins slapping tariffs on foreign goods and ignoring the World Trade Organisation.

In addition, any trade deal with the Trump administration is likely to be hard to swallow for Britain and would involve controversial concessions on the National Health Service and agriculture.

The British and American leaders also have profoundly different attitudes to international organisations. Mrs May is a firm believer in the importance of Nato and the United Nations. (Britain’s permanent membership of the UN Security Council is one of its few remaining totems of great power status). But Mr Trump has twice called Nato obsolete and is threatening to slash US funding of the UN.

The May and Trump administrations are also at odds on the crucial questions of the future of the EU and of Russia. Mr Trump is openly contemptuous of the EU and his aides have speculated that it might break up. This reflects the views of Nigel Farage and the UK Independence party — but not of the current British government.

Mrs May knows that her difficult negotiations with the EU will become all-but-impossible if member states believe that the UK is actively working to destroy their organisation in alliance with Mr Trump.

Her official position is that Britain wants to work with a strong EU. She probably even means it, given the economic and political dangers that would flow from its break-up.

Not the least of these dangers would be an increased threat from a resurgent Russia. The British government worked closely with the Obama administration to impose economic sanctions on the country after its annexation of Crimea. But Mr Trump is already flirting with lifting sanctions.

The reality is that the UK is now faced with a US president who is fundamentally at odds with the British view of the world. For all the forced smiles in the Oval Office last week, the May government certainly knows this. For political reasons, Boris Johnson, the British foreign minister, is having to talk up the prospects of a trade deal with Mr Trump.

Yet only a few months ago, Mr Johnson was saying that Mr Trump was “clearly out of his mind” and betrayed a “stupefying ignorance” of the world.

Were it not for Brexit— a cause that Mr Johnson enthusiastically championed — the UK government would be able to take an appropriately wary approach to Mr Trump. If Britain had voted to stay inside the EU, the obvious response to the arrival of a pro-Russia protectionist in the Oval Office would be to draw closer to its European allies.

Britain could defend free-trade far more effectively with the EU’s bulk behind it — and could also start to explore the possibilities for more EU defence co-operation. As it is, Britain has been thrown into the arms of an American president that the UK’s foreign secretary has called a madman.

In the declining years of the British empire, some of its politicians flattered themselves that they could be “Greeks to their Romans” — providing wise and experienced counsel to the new American imperium.

But the Emperor Nero has now taken power in Washington — and the British are having to smile and clap as he sets fires and reaches for his fiddle.

gideon.rachman@ft.com

Letters in response to this column:

Pragmatism will be lacking in US’s decline / From Prof Robert Holland, King’s College London, UK

Bilateral approach can only be beneficial / From Pierre Pelanne, Williamsburg, VA, US