Britain's new Chancellor of the Exchequer, Philip Hammond, waits to greet U.S. Treasury Secretary Jack Lew, at number 11 Downing Street in London, Britain July 14, 2016. [Photo/Agencies]

Chris Grayling, who ran May's leadership campaign, has also won a cabinet role as Secretary of State for Transport.

Earlier Thursday, the newly-appointed Chancellor Philip Hammond ruled out an emergency budget, which his predecessor Osborne had said would almost certainly be needed in the event of a vote to leave the EU. Hammond said there would be a normal autumn statement in the fall, and a regular budget next spring.

Hammond said in a media interview that the British economy was entering a new phase because of the vote to leave the EU, admitting the referendum decision of June 23 had had a chilling short-term effect on the economy.

"It has shaken confidence and caused many businesses to pause investment decisions that they were making," said Hammond, adding the government now needed to send signals of reassurance about the future as quickly and as powerful as it can.

The phone lines at Downing Street have continued to ring all day with messages of congratulation for May, who has become the second female prime minister in British history. Among the phone calls received by May were ones from German Chancellor Angela Merkel, French President Francois Hollande and Irish Taoiseach Enda Kenny.

May also had a 15 minutes telephone conversation with US President Barack Obama. May's spokeswoman said the prime minister "underlined her commitment to be a key partner with the United States."

Meanwhile away from intense media spotlight, the troubles continue for the main opposition Labour Party over its leadership battle.

Leader Jeremy Corbyn faces a leadership challenge from two of his MPs, Angela Eagle and Owen Smith. Most of Corbyn's shadow cabinet quit after 172 MPs passed a vote of no confidence in the leader.