The prime minister's appointment with President Donald Trump, a wildly unpredictable showman of very different political hue, could so easily have been awkward, even excruciating.

But it wasn't.

As the Downing Street team return to the UK, they are happy with how it went.

For some time senior figures were confident they had built a good rapport with Trump.

They had hoped too that his love of the UK and the depth of the long standing ties between the two countries would stand them in good stead - but they couldn't be certain.

Of course they couldn't be certain, because barely anyone ever can be with Trump.

I have been to the White House a handful of times before, but I have never been on a visit like this one.

Under President Joe Biden, us reporters would be invited into the Oval Office and then shown out minutes after we were shown in.

But Trump, as the BBC's state department correspondent Tom Bateman described it to me when I arrived, is currently governing by news conference.

He revels in the circus of performance and flurry of questions, his guests perched next to him occasionally chipping in, occasionally affecting a poker face - hoping there will be nothing said to them so outrageous they are forced to publicly contradict him.

For Sir Keir Starmer's visit, Trump cranked up the charm and the warmth.

The prime minister cranked up the superlatives and the compliments - and while not quite matching French President Emmanuel Macron's backslapping and knee grabbing, he was more tactile than I've ever seen him with any other leader.

Starmer leant into the theatricality beloved of his host, brandishing - with some performative flourish - the letter from King Charles inviting the president for another state visit.

It was stagecraft and statecraft combined in a single moment, neatly pitched for the scenario the prime minister found himself in.

The president's apparent endorsement of the government's plan to cede the Chagos Islands in the Indian Ocean to Mauritius and rent back the military base there on Diego Garcia - at considerable expense - was a perhaps unlikely fillip too.

But the idea still faces opposition at home.

The Conservatives question whether it serves the UK's national interest.

The proposed UK-US deal Trump made mention of is expected to be narrow, with an initial focus at least on the technology sector.

But there does remain considerable uncertainty about the practicalities of a peace plan for Ukraine.

The prime minister talked about the importance of "winning the peace" and not merely stopping the fighting.

The UK accepts there is no prospect whatsoever of American troops on the ground in Ukraine, but the government would like the US to provide air cover to protect British and other European peacekeepers.

Europe will need to be assured the US "has its back" is the gist of the argument being made.

But there has been no such public offer of air cover from the White House.

Instead, Trump has argued that the presence of Americans in Ukraine extracting the rare earth minerals expected to be part of the peace deal will be enough to ensure Vladimir Putin thinks twice before attempting further advances.

The security guarantees Ukraine wants will be a key focus at a summit on Sunday hosted by the prime minister in London.

He will meet Ukraine's President Volodymyr Zelensky and Italy's Prime Minister Giorgia Meloni in Downing Street in the morning, before hosting a gathering in the afternoon, to which more than a dozen other European leaders are invited.