If you thought it was bad enough when Donald Trump held a reluctant Theresa May’s hand, then look away now. For things are about to get sweatier.

The president’s clammy embrace of the British right continued this week with the arrival of his national security adviser John Bolton in London, to declare the most isolationist US regime in living memory would “enthusiastically” support a no-deal Brexit.

A weakened country, desperate for a trade deal and in no position to refuse Donald Trump’s demands not just to lower our stringent standards or hamstring our car industry but on foreign policy too? Step right this way, sir! No wonder Bolton talks of us being at the front of the queue for trade talks, a line every bit as clearly crafted to help Downing Street as President Obama’s suggestion during the 2016 referendum that Brexit would push us to the back of it. And if these presidents can’t both be right, then arguably neither can the two very different British Conservative administrations responsible for ghostwriting their respective lines.

We risk exchanging what leavers are fond of calling diktats from Brussels for diktats from Washington or Beijing

To some leave voters, all this will sound like sour grapes from people who can’t bear to admit that there might be life after Brexit. Many will actively share the Trump administration’s rejection of open borders and its distaste for rules-based international organisations, from the United Nations to Nato to the World Trade Organisation, which require sovereign nations sometimes to compromise or subjugate their own interests to the greater global good.

But as the former foreign secretary Jack Straw pointed out on Radio 4’s Today programme this morning, those organisations exist to check the potentially overwhelming clout of the biggest superpowers, in the interests of medium-sized and small countries who would otherwise be vulnerable. Brexit is rooted in a refusal to accept that Britain is now in the latter category not the former, and that we consequently risk exchanging what leavers are fond of calling diktats from Brussels for diktats from Washington or Beijing. Only this time we may not get a veto.

All trade negotiations naturally involve both sides trying to re-engineer things to their own advantage, of course. But the risks are heightened for small countries negotiating with bigger and more powerful ones – one reason EU countries banded together to do trade deals in the first place – and this time big foreign policy as well as economic principles are at stake.

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After his meeting with Boris Johnson, Bolton insisted that touchy issues like the Iran nuclear deal (which the US would like us to follow them in walking away from) or contracts with the Chinese tech firm Huawei (essentially ditto) could be left until “after Brexit”. But it’s naive in the extreme to imagine that they will be left until after trade negotiations have taken place – a process that is likely to take years. There is likely to be early pressure too to ditch practices that inconvenience American companies, such as Philip Hammond’s planned digital-services tax targeting tech giants who pay scandalously little in Britain. And Britain after a no-deal Brexit would be a beggar, not a chooser; a panicky minnow “negotiating” with a shark whose sole stated purpose is making sharks great again.

The real surprise isn’t that the White House actively favours a chaotic divorce between Britain and its European allies, irritatingly sceptical as the latter can be about US power that serves us up on a plate to Washington. It’s that the British government seems so trustingly inclined to go along with it.

• Gaby Hinsliff is a Guardian columnist