The two spoke on the phone today, and emphasised the need for NATO members to commit to spending two per cent of GDP on defence.
They also discussed Trump's transition plans, and planned to build close ties during his progression to the US presidency. As part of this, their national security advisors will be meeting in the US before Christmas.
A Downing Street spokesperson said: "The Prime Minister called the US President-elect this afternoon as part of establishing a regular dialogue between the both of them.
"They agreed to stay in close touch and to meet at the earliest possible opportunity."
Downing Street made no mention of Donald Trump's recent suggestion that Nigel Farage should be US ambassador. Trump made the outburst on Twitter, having met Farage in person twice since winning the US election. Downing Street was forced to respond to the tweet, saying that it had a perfectly good ambassador already.