May led tributes to Cameron at the meeting, which was described by ministers as “emotional”, and posed for photographers on the steps of the premier’s 10 Downing Street residence afterwards.
Cameron’s end came sooner than expected after dramatic twists in the contest to replace him led to his swift exit from power less than three weeks after the nation’s seismic vote to quit the European Union.
May will come under immediate pressure from EU leaders to set out a timetable for Brexit. The European Commission’s economy chief Pierre Moscovici urged May to accelerate the process.
“That’s what I think a lot of people expect and hope and call for,” he said in Brussels, adding that further delays would prolong damaging uncertainty for the economy.
German Chancellor Angela Merkel said late Monday: “The United Kingdom will need to quickly clarify how it wants its ties with the European Union to be in future.”
Cameron announced he would step down after leading the failed campaign for Britain to remain in the EU in the June 23 referendum.
Home Secretary May, the interior minister, was declared the new leader of the governing centre-right Conservative Party on Monday after junior energy minister Andrea Leadsom, her only remaining challenger for the post, withdrew from the contest.
May faces immediate questions on when she plans to trigger Article 50 — the formal procedure for withdrawal from the EU — which would set a two-year deadline for completing exit negotiations.
Before the leadership contest was cut short by Leadsom’s departure, she had said she did not foresee doing so before the end of the year at the earliest.
While May supported Britain staying in the bloc, she cut a low profile during the referendum campaign and insists she will honour the popular vote, stressing on Monday: “Brexit means Brexit”.
May also noted the need “to negotiate the best deal for Britain in leaving the EU” in brief comments outside parliament.
Cameron was to face MPs in parliament for a final time on Wednesday in the weekly prime minister’s questions session, before meeting Queen Elizabeth II to tender his resignation to the head of state.
The monarch will then call for May, the new leader of the majority party in parliament, to form a fresh government.
May, 59, will become Britain’s second female prime minister after 1980s Conservative titan Margaret Thatcher. She was to spend Tuesday sketching out who will take the key roles in her administration, which will be focused on delivering Brexit.
May will have to keep Leave-supporting Conservative heavyweights onside if she is to heal the splits in the party caused by the referendum. Removal men arrived at Downing Street in a blue van and began unpacking boxes.
One key figure who will be staying on in 10 Downing Street is Larry the cat, the Cabinet Office confirmed.
Meanwhile Tuesday was set to be a key date in the history of the main opposition Labour Party, whose embattled leader Jeremy Corbyn — hugely popular with the party membership — is facing a leadership challenge after losing the confidence of three quarters of Labour MPs.
The party’s ruling National Executive Committee (NEC) was to decide whether socialist veteran Corbyn would automatically feature in the contest after senior party figure Angela Eagle announced her leadership challenge on Monday.
The left-of-centre party’s rulebook states a leadership challenger requires the support of 20 percent of Labour MPs and members of the European Parliament.
However — crucially — it says nothing about whether the leader is automatically on the ballot or requires nominations too.
Corbyn, who would struggle to get 20 percent support, scrapped a planned speech at a conference of Unite, Britain’s biggest trade union and the party’s largest financial backers, to attend the NEC meeting.
Lawyers for Jim Kennedy, a trade union member of the NEC, have threatened immediate High Court action if Corbyn is not automatically put on the ballot.
There is a risk of the party splitting if Corbyn makes it on the ballot and secures a repeat of September’s landslide victory.