Up and down the avenues of New York City, billboards on bus stops and hotspot stations implore its denizens to cross the Atlantic for their holidays with pictures of favourite destinations like Edinburgh Castle, always with the recurring slogan about Britain being GREAT.

Making their wee speeches at an election-watch party at the British Consulate in Manhattan – distracting guests from the fine Indian buffet and news of returns on the BBC – UK diplomats meanwhile rehearsed the required line about “no two nations having more in common” and so on, complete with the usual chuckling reference to the time we set fire to the White House.

Well, I don’t know. Barely anyone in the country beyond the bounds of the Consulate and possibly a smattering of British-themed fish-n-chip pubs paid the blindest bit of attention to the political tremors going on in ye olde country. This would be on account of their having a few of their own to contend with. Comey commands the headlines here, not Corbyn or Clegg.

And Britain, after all, is confusing. Americans have seen more of Nigel Farage than they have of Theresa May, because of his past palling around with Donald Trump. They will watch a bit of Wimbledon and, who knows, they might take that trip. Because, GREAT should really read CHEAP, when you consider the fresh battering the pound took early Friday against the dollar.

What may sink in about the UK election results is a vague sense of additional unease about the state of the world at a time when everyone surely needs less of it. Britain has been the most important sinew in the post-World War II bond of democracy and economic prosperity between the US and all of Europe. That that connection seems in various ways to have frayed is good news for no one.

Barack Obama has some responsibility for making the special relationship somewhat less so. It wasn’t just the flap over removing Winston Churchill from the Oval office. (The old boy’s back now, of course, in all his dulled-bronze and glowering splendour.) He deliberately turned America’s gaze east and south towards Asia and in so much as he paid heed to Europe it was more to Merkel than to Cameron or Brown. Maybe after Brexit, he considered that smart.

It was Obama who warned Britain that leaving Europe would mean it going to the back of the queue for a new trade deal with America. He was widely criticised for it and even blamed for stoking anti-Leave sentiment ahead of Britain’s referendum. But there is no reason to assume he was wrong or that when negotiations for such a deal begin, the Trump administration will be anything but tungsten-tough in its stance. You saw what Trump told Germany about selling too many cars in America. Flipping trade flows to America’s advantage is the heart of brand Trump.

And as much as Trump appears to dislike regional trade treaties – he wants to tweak Nafta with Canada and Mexico and has put the kibosh on the Trans-Pacific Partnership, TPP – it remains the case that when it comes to looking eastward the priority for his trade negotiators will be the putative Trans-Atlantic Trade and Investment Partnership (TTIP) with the European Union even if for the moment talks have stalled. Britain, presumably, won’t be part of it.

Put together the irritations in the US-UK relationship amount to a malaise, meanwhile. Some are multi-lateral in nature. Let’s leave aside consideration of whether Britain departing the European Union will make it a bigger or lesser force in the world, even if it’s hard to make an argument in support of the former. But which British leader would have ever imagined being lectured outside Nato headquarters by a sitting American president about defence spending levels while at the same time hearing nothing from him about the Alliance’s mutual defence provisions?

We meanwhile have the highly unusual spectacle of Britain publicly squabbling with the US in the sphere of intelligence-sharing – for years at the very heart of the security relationship between them – because of the apparent leaking by US officials to the American media of details of the police investigation in the immediate aftermath of the Manchester arena bombing. Trump promised to deal with that but only because stopping leaks is something of a fetish with him.

Still more dispiriting was Trump’s toxic sniping at the Mayor of London, Sadiq Khan, straight after the terror attack just a week ago at Borough Market. You may recall, he suggested that the leader of the nation’s capital had been “pathetic” in his response to the crisis. He willfully took Khan’s words out of context by suggesting he’d said Londoner’s shouldn’t be alarmed by what had happened and did it via Twitter, naturally. “It was stunning for all us in America, and indefensible,” former CIA and National Security Agency head Michael Hayden sputtered in The Guardian. Khan was himself withering in return. “I don’t know how to tell you this, but I really don’t care…I really couldn’t be bothered about what Donald Trump tweets.”

There are more tests to come. Khan was also asked about that other small matter on the horizon – a state visit by Trump to Britain for tea with the Queen and whatever else May lays on for him. If May is the host, of course. Maybe put him on a polo horse. Or in the Tower of London. Khan said it should not happen and there are many, in Parliament and elsewhere, who share the sentiment. When the time arrives, Trump’s visit, unless a way is found to shelve it, is likely only to highlight how strained the so-called special relationship has become.

Some will meanwhile try to discern some greater electoral meaning from the shock outcome of the British vote. Did May’s failure to distance herself more from Trump harm her? Should Corbyn have gone the full Bernie Sanders? And what about for America and its current political maelstrom? Does the faltering of the hard-Brexit Tories spell an ebbing of the populist tide for Trump, who continues to play the isolationist-America First card with his base?