There is also speculation that May, Britain’s second female prime minister after Margaret Thatcher, will boost the number of women in top posts.
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Speaking outside 10 Downing Street after being appointed by the Queen, May, 59 said it would be her mission to “build a better Britain”.
Cameron said Britain “is much stronger” than it was when he first became Prime Minister in 2010 – highlighting his government’s efforts to improve the economy, as well as flagship policies such as the national living wage, reforms to the adoption system and the legalisation of gay marriage.
Cameron will formally tender his resignation to Queen Elizabeth II at Buckingham palace later in the day.
She also paid tribute to her predecessor, David Cameron, saying he had been a “great, modern prime minister”.
Though she joined Mr. Cameron in supporting continued European Union membership, Ms. May assured the public on Monday that “Brexit means Brexit”.
Conservative lawmaker David Davis will take the newly formed job of minister in charge of negotiations with the European Union that will set up the conditions for leaving.
Her continental peers have said they expect her to move quickly to implement the referendum result.
Germany’s Angela Merkel, France’s Francois Hollande and Italy’s Matteo Renzi announced Wednesday that they will hold a summit in August on the matter.
Congratulations came from all sides in Parliament, but some expressed concern given her tough stands over the past five years as the equivalent of Britain’s homeland security chief.
Johnson had been at the forefront of the so-called Leave campaign, but after its triumph abruptly pulled out of the contest to succeed Prime Minister David Cameron, who left office earlier Wednesday.
He replaces Philip Hammond, who becomes chancellor.
Her government will fight against “burning injustice” and will prioritize ordinary people over the interests of the wealthy, she said.
She is under pressure from pro-Brexit Conservatives and other European Union leaders to start formal exit talks with the bloc.
The last few weeks have been dramatic ones in British politics, with Brexit setting off a domino effect of politicians falling by the wayside – Cameron resigned, allies stabbed likely successor Boris Johnson “in the back”, and leadership contender Leadsom threw in the towel amid controversial motherhood comments.
A majority in Scotland voted for Britain to remain in the EU.
Writing on Twitter, South Wales East Mohammad Asghar said Mr Cameron would be “sadly missed” and it was “a true pleasure” to serve as a Conservative politician under his leadership.
Cameron had called the referendum and campaigned to stay in the European Union in a bid to try to heal divisions in the Conservative ranks.
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“I don’t detect Theresa May being an impulsive person”, Travers said.
