In a sprawling interview with the Wall Street Journal this week, Donald Trump said: “I don’t know what the word permanent means”, adding that he could give 20 examples in his life of deep enmities and “then all of a sudden somebody’s my best friend”.

Caprice in his alliances and policy-making is clearly seen as a strength by the US president. The former British foreign secretary Jack Straw, for instance, said a decision expected on Friday on whether to lift the sanctions waiver on the Iranian nuclear deal came down to the flip of a coin in the Oval Office.

So reading too much about the health of the Anglo-American relationship on the basis of one eminently reversible decision by Trump not to visit London next month is unwise. Even to ask: “What did he mean by that?” could be elevating a mood into a thought process.

The stated reason – that Trump did not wish to bless a bad real estate deal struck by Barack Obama – is not plausible. The deal was not struck by Obama, and the US ambassador Woody Johnson, a loyal friend, was expecting Trump to come to London to cut the ribbon.

Nor can the plan to travel to Switzerland this month to speak at the Davos economic summit, so requiring two transatlantic trips in as many weeks, be sufficient reason. Trump was willing to make a Bastille Day visit to Paris to be greeted by the French president, Emmanuel Macron, only two weeks after going to Poland, Germany and Brussels on a visit built around a G20 summit.

So there is something the UK is not getting right in its relationship, and much stems from Theresa May’s premature offer of a state visit before Whitehall and Buckingham Palace had absorbed the extent to which the new occupant of the White House was not just another Republican slightly to the right of George Bush.

Set against the prospect of the proffered state visit, with its full flummery, the allure of a noisy visit to London for a working lunch with the British prime minister must have palled, especially if it was to be followed by a trip to Wandsworth to open an overpriced “off location” office block that he does not own.

Worse still, it is possible that Obama, Trump’s predecessor and bugbear, could in a few months enjoy the spring glamour of a royal wedding at the personal invitation of Prince Harry. The contrast might have been too much for a vain man to bear.

The most worrying interpretation of the non-visit, and the one that will keep the Foreign Office awake at night, is that Trump does not care that much about Britain. Despite Brexit, the UK may in his mind be being gradually lumped into the mass of European countries opposed to what he represents, not just on issues such as migration and multicultural relations, but also on trade.

In recent months, on foreign policy – the Iranian nuclear deal, the isolation of Qatar by Saudi Arabia, the recognition of Jerusalem as the capital of Israel – the UK has also sided with its European partners and against Trump’s decisions. The UK even voted against him at the UN security council on Jerusalem, despite a warning by the US ambassador to the UN, Nikki Haley, that names of America’s opponents would be taken, and remembered.

The US and the UK have also struck a different tone on Iran. Similarly, the UK is much more willing to denounce Russian cyber-interference in European elections.

All these policy disagreements can be exaggerated. UK-US differences over the Middle East were as alive in the Thatcher-Reagan era, and on the big call about the aggressive nature of the existing Iranian regime, the UK would largely side with America and Saudi Arabia. The intelligence relationship continues to flourish and as many as 400 UK personnel are embedded in the US military.

But however much the UK insists the relationship has always been based on a respect for the office of the president, not the president himself, these are not the easiest times. May recently famously warned the Russian president, Vladimir Putin: “We know what you are doing.” She probably fervently wishes she could say the same about President Trump.