Dozens of Conservative MPs have backed her bid to take over from Cameron, who announced his resignation after losing a referendum last week in which 52 per cent of Britons voted to quit the EU.
Britain has been plunged into extraordinary political turmoil since the Brexit vote, with the ruling Conservatives and opposition Labour party in disarray and the country deeply polarised.
In further signs of economic fallout, finance minister George Osborne warned that London will likely abandon a key budget promise, while budget airline EasyJet announced plans to ensure its European operations after Brexit.
The Daily Mail newspaper, widely read among Conservative grassroots who will ultimately select the new leader, endorsed her with a front-page headline saying: "A party in flames and why it must be Theresa".
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EU leaders have called for a swift divorce following last week's seismic vote, fearful of the impact of Britain's uncertain future on economic growth and a potential domino effect in eurosceptic member states.
"The decision has been taken, it cannot be delayed and it cannot be cancelled, now they have to face the consequences," French President Francois Hollande said after meeting Cameron on the sidelines of Battle of the Somme centenary ceremonies in France.
The outcome of the June 23 vote unleashed the worst chaos in living memory in British politics, with opposition Labour leader Jeremy Corbyn's leadership also under threat and Scotland's government fighting for independence to keep its EU membership.
Justice minister Michael Gove, a top Brexit campaigner who torpedoed former London mayor Johnson's chances by announcing his own candidacy yesterday, is seen as May's main rival.