Britain was seeking to fast-track a crucial post-Brexit trade deal with the United States on Wednesday after new Prime Minister Boris Johnson dispatched his top diplomat and foreign trade minister to Washington.

Foreign Secretary Dominic Raab was due to hold talks with  US Secretary of State Mike Pompeo at the State Department while the International Trade Secretary Liz Truss has lined up meetings with top American trade officials.

With Johnson determined to ensure Britain leaves the European Union on October 31, with or without a deal, striking some kind of trade accord with the Trump administration has taken on even greater importance.

Trump, who sees a like-minded leader in Johnson, has said that trade between the two countries could multiply once Britain leaves the EU and spoke to the British prime minister about a deal within days of his taking office last month.

"Negotiating and signing an exciting new free trade agreement with the US is one of my top priorities," said Truss, who was a cheerleader for the leave camp in the 2016 referendum on Britain's membership of the EU.

"Having already laid the groundwork, we are fast-tracking this deal so that businesses are able to take advantage of the golden opportunity to increase trade with the US as soon as possible," she added.

"The US is our biggest trading partner and we have more than $1 trillion invested in each other's economies. We want to get formal talks moving quickly."

Truss met with US Trade Representative Robert Lighthizer on Tuesday and will meet Commerce Secretary Wilbur Ross later in the week, US officials said.

After his first phone call with Johnson, Trump told reporters that a bilateral deal with post-Brexit Britain could be "three to four, five times" bigger than current trade and once London is out of the European Union "we could do much more."

"We're working on a trade agreement already," Trump said. "I think it will be a very substantial trade agreement."

Johnson, clearly enjoying warmer relations with Trump than his predecessor Theresa May, is hoping that he can clinch a swift deal that can send a message of Britain's ability to strike out on its own.