During the May-Trump press conference, the US president was as baffling as ever

In between piling an absurd weight of praise on the prime minister, casually attacking Germany and bragging about the Nato summit, Mr Trump offered the hope of a better relationship with Vladimir Putin

Like the Trump baby blimp floating around in the skies above Westminster, Mr Trump’s rhetoric was pretty inflated

During the Trump-May press conference at Chequers, ITV journalist Robert Peston asked President Trump to calibrate the specialness of the relationship between America and Britain, perhaps hoping for some sort of lukewarm response. Spotting the trap, President Trump stepped on the gas. He asked the assembled journalists if there was anything higher than “the highest level of special”. On confirmation that he had indeed reached the verbal summit at this political summit, the president settled for that.

Mr Trump looked pleased with this bare-faced defiance, as ever. Theresa May, not naturally given to hyperbole, just displayed a blend of relief and embarrassment, as if the insincerity of it might appear just a bit too obvious. Like the Trump baby blimp floating around in the skies above Westminster, Mr Trump’s rhetoric was pretty inflated.

If only the special relationship was actually operating at such stratospheric levels of specialness. What seems to have happened is that Mr Trump had reverted to his usual, baffling pattern of behaviour before meeting other world leaders. It runs roughly as follows: Mr Trump gives an interview or throws some off-the-cuff remark out during a press conference, or thumbs out a tweet that deeply offends an honoured ally or deadly enemy alike.

Then the opportunity, or obligation, arises for Mr Trump to meet that ally, possibly after some strong diplomatic protests. When he is physically next to them, he then rows back and uses a mixture of bluster, denials and generalised flak about “fake news” to claim that relations are actually the best they could ever be, and he had never suggested otherwise. Then he insults someone else (yesterday it was the turn of Angela Merkel; Vladimir Putin was let off with faint praise). A couple of US news organisations were called “fake news”. No Trump presser could be judged complete until he’s roughed up some of the media. Then he’s back on Marine One.

Such has been Theresa May’s fate as she was put through the emotional wringer, again, this time a result of an interview in The Sun. In the morning she was a poor substitute for Boris Johnson, was an incompetent negotiator, and her Brexit white paper had virtually killed any trade deal with the US. By the early afternoon we were through the looking glass again, and into a world where the prime minister wasn’t some sort of sub-Boris weak loser, but, standing next to the president, was, rather “an incredible woman doing a fantastic job”.

The same cycle, more importantly, was applied to the prospective US-UK trade deal. After a chat to Ms May and British officials, Mr Trump was prepared to resurrect an “ambitious” and “great bilateral trade agreement”, but this Trump declaration was, for a change, a little more nuanced.

Pleading that the Brexit talks were a matter for the British, he merely entered a plea that the resulting EU-UK trade treaty would allow the US to have a trade deal too – and one that would “double, triple, quadruple” trade. That will depend on whether the EU-UK “common rule book” would allow, for example, US foodstuffs into the UK – genetically modified produce included. Ms May said that would be for the negotiations.

Second, Mr Trump used the phrase “even trade” in regard to US-UK trade, which is ominous, given that the British actually enjoy the luxury of a trade surplus with the United States. As with his other trade partners, “special” or not, Mr Trump’s principal aim is to put America first and to reduce the other nation’s trade surplus. So the British might well – if the EU rulebook can be bent to allow it – enjoy a greater volume of trade with the US, but it would come at the cost of a smaller trade surplus with America. So the net effect of Brexit may be to actually reduce the UK’s £34bn trade surplus with America, the largest run by the UK with anyone in the world.

In between piling an absurd weight of praise on the prime minister, casually attacking Germany and bragging about the Nato summit, Mr Trump offered the hope of a better relationship with Vladimir Putin, and acknowledged the difficult issues he would have to bring up in Moscow – Ukraine and the occupation of Crimea, Syria, nuclear proliferation, and, with no hint of irony, the Kremlin’s “meddling” in foreign elections.

He did not, however, entirely dispel the impression that he might attempt to negotiate a grand compromise with the Russians that would involve them being given a freer hand in Ukraine in return for Russian support in restraining Iran, particularly in Syria, and a reduction in nuclear arsenals. We will see quite how special, on the Trump scale of specialness, his relationship with Vladimir Putin turns out to be – and how dangerous it will be for the world.