In Donald Trump’s White House the vibes really matter. The personal relationships he develops with other leaders can affect how those nations are treated.

So it was vital for British Prime Minister Keir Starmer to not only master the details of their discussions but to build a rapport with the US president.

The invitation from King Charles clearly set the right tone. Trump looked truly flattered that he would become the first person to enjoy a second state visit to the UK.

“And that’s a great honour, because it’s never happened before,” the president said at the start of their joint news conference. “I really do call it an honour, but it’s not for me, it’s for our country. It’s respect for our country.”

The very diplomatic language deployed by Sir Keir over Ukraine – like praising Trump for creating the conditions in which a ceasefire is being discussed – could not disguise the disagreements over what a peace deal may end up looking like.

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The warm atmosphere and friendly body language we saw when the two men first met in the Oval Office just before lunch did not seem quite so pronounced when they emerged after talks about three hours later.

“You are a very tough negotiator… I’m not sure I like that, but okay,” Trump told Sir Keir as they appeared before reporters after their meeting. And he did not seem to be entirely joking.

On the prospect of trade tariffs being imposed on UK exports to the US, the prime minister did seem to have made some progress.

Trump said Sir Keir had worked hard and “earned whatever they pay him over there” when he made the case for a trade deal between the two countries instead of tariffs. That would count as a significant victory for Britain, though any proposed deal would inevitably require lengthy and detailed negotiations.