The two leaders spoke for the first time a week ago, with new details of the ten-minute telephone call being revealed by the Times.
Mr Trump told the Prime Minister that his mother Mary MacLeod, who emigrated from the isle of Lewis to New York in 1930, was a “big fan” of the Queen, and asked Mrs May to pass on his regards on her next trip to Buckingham Palace.
During the call, Mr Trump said the UK was a “very special place for me and my country”.
In a more informal invitation than is traditional between world leaders, the president-elect told Mrs May to visit him if she was ever in the neighbourhood. “If you travel to the US, you should let me know,” he said, according to a leaked transcript.
Following comments by the Trump campaign that Muslim visitors could be barred from the US and immigrants subjected to “extreme vetting”, yesterday SNP MP Tommy Sheppard asked Mrs May what action she would take if “the new president-elect carries through his campaign promise to discriminate against our citizens on the basis of their religion?”
During Prime Minister’s Questions, she replied: “Of course we want to ensure the dignity of our citizens. It is up to the United States what rules it puts in place for entry across its borders but we will ensure that the special relationship continues, and does so in the interests of both the UK and the US.”
It was also reported that a call between the Australian Prime Minister and Mr Trump only took place after Malcolm Turnbull was given the president-elect’s private mobile phone number by golfer Greg Norman.