Chris Mason: From inside the room, how Burnham survived first Trump meeting

As I crouched between the cameras, determined to catch Donald Trump's eye and ask a question, I listened to a president seeking to be magnanimous.

Remember, Trump can and does do warmth when he wants to, as well as acerbic.

Prime Minister Andy Burnham, a mayor a matter of months ago, sat next to the most powerful man in the world.

Put like that, it sounds believable when he said in advance he was looking forward to the meeting, but there must have been a jab of nerves too.

Burnham did look a little nervous as us reporters trooped into the room, but then, for the most part, the compliments flowed from the president.

The original plan was for journalists to be invited in at the beginning of the meeting, perhaps just minutes after the men had first met.

Instead, we were kept waiting while the private talks took place, which came with the upside that they had more to say about each other and what they had discussed than would otherwise have been the case.

Burnham knew, the world knows, how explosive these rolling, free wheeling, live on camera encounters with Trump can go.

It is rollercoaster without a harness stuff.

Having got myself into the president's eyeline, I waited for the last syllable of Burnham's final word at the end of his opening remarks and I filled the brief silence with a question.

Was the prime minister a man you can do business with, I asked the president, given your political differences?

"I do, I think he's a natural business person. We've had a lot of discussions even before this meeting. We've spoken to each other numerous times on the phone. Yeah, I think so, I think so. He gets it. He understands what he has to do."

The warmth was self evident. Perhaps the Downing Street nerves will have eased a bit.

But how long would the questions keep going? This is the president's theatre and he decides how long the public performance lasts. On occasion they are way north of half an hour.

This was a meeting on neutral territory, a windowless, non descript meeting room down a dingy corridor in the basement of the United Nations. This wasn't the Oval Office of the White House. Perhaps that dialled down the sense of occasion a notch.

Nonetheless, for how long could the president maintain the bonhomie and sense of agreement? A question about immigration, potentially a point of friction, came and went without incident. So to did the Burnham government's decision, announced by the Foreign Secretary Ed Miliband, who was in the room, to sanction settlements in the West Bank, a decision which infuriated Israel.

But on the future of the Chagos islands, the president couldn't hide his view that Britain's decision to cede sovereignty of them to Mauritius and then rent back the military base on Diego Garcia was "terrible."

The president added: "I think the prime minister is going to be looking at [the deal]" and Burnham replied "yep".

Ah, interesting.

Later, it was my turn to do a short interview with the prime minister on behalf of all of the broadcasters.

Burnham emphasised that the meeting was "very encouraging" and "we've established a good connection."

But what about the Chagos deal? Would it change, I asked. Pointedly, he described it as a deal he had "inherited".

"We've got to find a resolution, and so work will continue now…to see where that resolution might lead."

In other words, it looks like it is going to change.

Flashpoints down the track with Trump are near inevitable — barely any leader avoids them with this administration, and Burnham may want to lean into some, in time.

And even those he doesn't might lean into him, Chagos possibly one of them.

But outwardly Burnham has a relationship with the president he can now build on after this opening face to face conversation.

What followed in the prime minister's remaining meetings at the UN were diplomacy by convention, not the wild ride with Trump he had just stepped off and survived.