WASHINGTON (Reuters) - Evoking the closeness of U.S. President Ronald Reagan and British Prime Minister Margaret Thatcher, Theresa May and Donald Trump shared a “warm conversation” at lunch on Friday to cement their own “special relationship”, a source in May’s team said.

U.S. President Donald Trump escorts British Prime Minister Theresa May after their meeting at the White House in Washington, U.S., January 27, 2017. REUTERS/Kevin Lamarque

May’s visit to the United States, the first by a foreign leader since Trump was inaugurated as president, has been hailed by her aides as a resounding success, one, they say, that has strengthened her hand in divorce negotiations with the EU.

A statement from May’s office said Trump pledged to ensure that the trade arrangements that Britain currently has with the U.S. through its membership of the European Union will continue in place the moment it leaves the bloc.

It was not clear how Trump’s aides viewed the meeting on Friday when the two leaders held talks and then had a lunch of baby iceberg salad with blue cheese and braised beef shortribs, but the UK delegation saw the visit as a triumph.

“They talked a lot about Thatcher and Reagan, and both agreed it was one of the most successful political relationships ever,” the source in May’s team said. “Trump went on to say that he always looked up to Reagan and said that he wanted their relationship to be even better than that one.”

Ties between Britain and the United States struck a highly personal tone under Thatcher and Reagan in the 1980s, with the image of them dancing at a ball at the White House epitomising the trans-Atlantic “special relationship”

On paper, May and Trump seem poles apart.

The British leader is a cautious politician, a vicar’s daughter who uses words very carefully, while he is a boisterous former reality TV host whose comments on Twitter have often sent shockwaves around the world.

But, according to the two leaders at a news conference on Friday, they struck up a rapport.

Describing their conversation over lunch as “warm, free-flowing and unscripted”, the source said the two leaders not only discussed their “shared admiration” of Reagan and Thatcher, but also Brexit, Russia and the NATO military alliance.

TRADE PROMISES

On trade, they discussed ways to prepare for a deal for after Britain leaves the European Union, including setting up a trade negotiation agreement that will involve high-level talks to scope out what can be achieved before Brexit.

“President Trump pledged to ensure that the trade arrangements that the UK currently has with the U.S. through its membership of the EU will continue in place at the moment the United Kingdom leaves,” May’s team said in a statement.

May said it was “a step forward that underlines our commitment to use the opportunities of Brexit to build a truly global Britain, increase free and fair trade, and improve the special relationship between our two great countries”.

But some critics said May had ducked contentious issues to win promises for future trade - a charge repeated when she arrived in Turkey on Saturday to strengthen ties with President Tayyip Erdogan, who has been criticized by rights groups for jailing tens of thousands of people after a failed coup in July.

“Who knows what Theresa May has secured here apart from vague platitudes?” leader of the Liberal Democrats, Tim Farron, said in a statement. “Theresa May clearly spent her time with Trump dodging his despicable comments.”

But while questions were asked about Britain’s charm offensive, her aides welcomed Trump’s comments, including his description of May as a “people person”.

The source said at the end of Friday’s lunch Trump announced that he always kept menu cards to remember significant moments.

“He gave the menu card to one of his members of staff and said ‘keep that safe, I had lunch with the British prime minister’.”