British Prime Minister Andy Burnham and US President Donald Trump meet in New York, discuss Ukraine, Falklands, trade

British Prime Minister Andy Burnham and US President Donald Trump appeared to get along well as they met for the first time in New York this week.

The leaders gave short statements and took questions from the media on the sidelines of the United Nations General Assembly on Tuesday after holding talks together.

Trump, who remained polite and friendly throughout, opened by saying he thought Burnham was going to be a "great prime minister" and that he had "a lot of assets on his side," adding that the US was with him "all the way."

In response, Burnham thanked the president before touting their "good connection," while noting that the pair had discussed Ukraine, the Falkland Islands, and trade issues in their discussion.

Asked whether Burnham was someone he could do business with, Trump seemed positive, describing him as a "natural businessperson" - a label that might raise eyebrows among some of the prime minister's critics at home.

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

On immigration, a politically charged topic on both sides of the Atlantic that has been central to Trump's presidency, Trump gave a diplomatic response despite having previously delivered strong criticism of the UK's approach to the issue.

For his part, Burnham acknowledged the growing importance of immigration in British politics and noted that the UK was continuing to tackle migrant boats arriving from continental Europe. He added that crossings were down roughly 50% over the summer compared to six years ago.

Trump wrapped up the news conference with a jab at former British Prime Minister Keir Starmer, saying that relations with the UK were "more up now" under Burnham while also slamming the Starmer government's Chagos Island's deal as "terrible." The proposed deal would give Mauritius sovereignty over the islands, which include the UK-US Diego Garcia military base.

"Right now, based on my relationship with your prime minister, Andy, I think we're doing very well," Trump said.

Burnham, who took office in late July, seems to have established a foundation he can build on with regards to his dealings with Washington, and he will likely be pleased with how the conference went given how unpredictable some live events with Trump can be.