“Opposites attract”, so the Prime Minister thinks (the evidence of that, as many divorced couples can attest, is mixed). Whether Donald Trump and Theresa May do develop the sort of “fantastic relationship” the President is promising very much remains to be seen.

During their public session the signs were hard to read. Ms May is as habitually nervous in public as Mr Trump is confident, and there were some awkward moments, although it was mostly a convivial sort of day. During the press conference President Trump managed to speak on behalf of the Prime Minister when he was asked about his Mexican standoff with President Enrique Peña Nieto. It was a casual act of chauvinism that said much about Mr Trump, but was graciously skated over by Ms May.

So far as a deal is concerned, Mr Trump wangled a public invitation for a state visit to the UK later this year, complete with the usual pomp, ceremony and photo opportunities with the Queen. In return Mr Trump allowed Ms May to tell the world that he is “100 per cent behind Nato”, a little condescending on her part that time, but a relief to nervous Europeans.

Mr Trump himself declared that although he believed “torture works”, he would defer to his new Defence Secretary. In turn he was effusive about Brexit – “a wonderful thing” – and they succeeded in limiting their disagreements about Russia and Iran. Mr Trump’s openness about how his relationship with President Putin might evolve and his surprisingly warm wish for a strong relationship with China was also encouraging.

Perhaps, then, there is something in the spin, and that this odd couple will indeed “lead the world” once again, but will engage in open and frank discussion with one another as only close friends can. Mr Trump was certainly more subdued and guarded in his remarks than usual. He stuck to his script, apart from a sideswipe at the BBC’s Laura Kuenssberg (clearly not his type).

But a clear, generous and open commitment by the American President to a trade deal with Britain was conspicuous by its absence. The warm words were certainly there, and no end of goodwill, but Mr Trump, shrewd dealmaker as he claims to be, has no hostages to fortune about the UK-US free trade deal. Indeed, Mr Trump made it apparent that he will, as ever, be representing the American people in a tougher fashion than his predecessors.

On defence, security and intelligence there was an easy agreement, and these are early days in the “renewal” of the so-called special relationship. The reality behind this Anglo-American diplomacy keeps poking through, however: America will be fine with the UK so long as our vital interests continue to coincide. We can agree to differ on the smaller stuff, but there should never be any doubt that, from trade to the nuclear deterrent, Britain needs America more than America needs Britain.