Theresa May has finally spoken with Donald Trump, after criticism that their failure to talk had left Britain somewhere near the “back of the queue”.

The two leaders had a telephone conversation at 1.45pm, Downing Street said, focusing on the UK-US “special relationship” and on strengthening bilateral trade.

A No 10 spokesman said: “The Prime Minister and President-elect Trump agreed that the US-UK relationship was very important and very special, and that building on this would be a priority for them both.

Theresa May 'looks forward' to working with Donald Trump

“President-elect Trump set out his close and personal connections with, and warmth for, the UK. He said he was confident that the special relationship would go from strength to strength.”

The spokesman added: “The call ended with President-elect Trump saying that the UK is a ‘very, very special place’ for him, and inviting the Prime Minister to visit him as soon as possible.”

The conversation came after the embarrassing revelation that Mr Trump had already spoken with at least nine other world leaders, apparently leaving claims of a special relationship in tatters.

In just 24 hours after his victory, he spoke with the leaders of Egypt, Ireland, Mexico, Israel, Turkey, India, Japan, Australia and South Korea.

By the time he chatted with Ms May, Mr Trump had invited the Irish Taoiseach Enda Kenny to the White House for St Patrick’s Day next year.

And he had arranged to meet Shinzo Abe, the Japanese Prime Minister, next week before an Asia-Pacific Economic Cooperation (APEC) summit.

Chancellor Philip Hammond raised eyebrows when he suggested Ms May and Mr Trump had not yet spoken because they had no “urgent business” to discuss.

Last month, the Republican’s trade adviser said that under a Trump presidency Britain would come first in any trade talks between the US and Europe, after Barack Obama had said during the EU referendum campaign that the UK would be at the “back of the queue” if it chose to vote Brexit.

The Trump camp has said it has “no immediate plans” to travel to Britain or Europe ahead of his January inauguration.

The American and British leaders will meet at the next G7 summit, in May next year, and Ms May hopes to be invited to Washington before then, to discuss a possible post-Brexit trade deal.

Tim Farron, the Liberal Democrat leader, tweeted: “Trump yet to call May, but has called Egypt Ireland Mexico Israel Turkey India Japan & Australia...almost like we are ‘back of the queue’.”

Mr Trump – who recently bought a golf course in Ireland reportedly worth £12.4m – quickly found time to speak with Mr Kenny and invite him to America. The tradition of a get-together with the Taoisigh on St Patrick’s Day would continue “in the spirit of the strong ties between the two countries”, Mr Trump said.

Mr Kenny said: “I had a very good conversation with the President-elect. He understands Ireland very well, he was complimentary about the decisions made about the economy here. He is looking forward to doing business with Ireland.”

Mr Trump also pledged his commitment to defend South Korea, during a phone call with its President Park Geun-hye, a news agency in the country said.

And Turkish President Tayyib Erdogan wasted no time in congratulating the President-elect and discussing “the future of his country's relationship with the US”, Ankara said.

Malcolm Turnbull, Australia’s Prime Minister, and Mr Trump spoke for 15 minutes on the telephone, covering trade, regional security and the fight against Isis.

A statement from the Egyptian presidency said Abdel Fattah al-Sissi was the first world leader to have a conversation, which focussed on how to “foster closer diplomatic ties”.

In the hours after the result, Germany's Angela Merkel and France's Francois Hollande offered Mr Trump only cautious support – warning that his win ushered in a “period of uncertainty”.

But Ms May ducked questions about past criticisms of his stance on Muslims, saying: “Britain and the United States have an enduring and special relationship based on the values of freedom, democracy and enterprise.