British Prime Minister Keir Starmer is expected to meet Donald Trump at the United Nations General Assembly next week, as a new agreement over Greenland draws political reaction in the UK.

Speaking at the Liberal Democrat party conference, Andy Burnham dismissed Trump's claims of a diplomatic victory over Greenland, arguing the deal amounted to little more than a restatement of existing arrangements.

"Donald Trump is trying to claim he's got a success in Greenland, but actually, all he's got is almost a carbon copy of the agreement that's persisted since the 1950s," he said.

"So let Donald Trump try to pretend he's had a victory. The truth is, Europe, Nato, countries like Canada stood up to him and won."

Trump had for months threatened to purchase or annex Greenland, the semi-autonomous Danish territory, arguing it was vulnerable to adversaries including Russia and China.

Danish Prime Minister Mette Frederiksen said she was "pleased that there is a prospect of a good agreement" for all three parties involved. The deal is expected to be signed at the UN General Assembly next week.

The agreement "strengthens our common security in the Arctic and the North Atlantic area" while also recognising "the sovereignty and territorial integrity of the kingdom and the right of the Greenlandic people to self-determination," Frederiksen said in a joint statement with Greenland's Prime Minister Jens-Frederik Nielsen.

The statement noted that the agreement would still need to go through "the necessary parliamentary procedures to enter into force" once signed.

Downing Street said the Prime Minister has spoken to Trump at least twice since taking office and intends to use the UNGA to "drive forward work on issues that matter to people at home," including the cost of living and the war in Ukraine.