The Conservatives feel themselves lucky in their opposition: The unlikely new Labour Party leader, Jeremy Corbyn, is from the hard left and has deeply divided his own party, while the Liberal Democrats, with whom the Tories were in coalition for five years, were clobbered by voters in May’s election.
In some sense, the main challenge to Mr. Cameron is from inside his own party, and the weakness of the opposition gives extra room for party indiscipline, at least for now.
The Tories have been divided over membership in the European Union for a generation, and on Sunday, Mr. Cameron conceded that his efforts to renegotiate ties with Brussels were proving very difficult — “bloody hard work,” he told the BBC.
While he is known to favor remaining in the European Union, he is trying to manage the large minority in his party who want out, their position bolstered by the mess over Greece’s finances and this summer’s continuing chaos over migration.
On Sunday, Mr. Cameron refused to rule out campaigning for a British exit in a referendum on membership, promised to his euroskeptics and due by the end of 2017 (though expected sooner), if other European leaders failed to grant him the concessions he wanted.
But those concessions, which largely have to do with protecting the City of London, Britain’s freewheeling financial center and trying to limit immigration even from European Union citizens, may require treaty changes and will not be easy to achieve in the time frame he desires.
“But I am confident we will get what we need,” he said, asking for patience. But the “out” campaign is gathering pace, with one well-known former Conservative chancellor of the Exchequer, Nigel Lawson, leading a group that says there is no point waiting for Mr. Cameron to finish what will be disappointing talks before organizing the campaign.
Nigel Farage, the leader of the U.K. Independence Party, or UKIP, which wants to leave the bloc, has also been vocal about campaigning now for an exit, but he will probably play a secondary role to more established figures like Mr. Lawson, who served under Margaret Thatcher.
Asked if Britain was drifting toward a “Brexit,” or exit from the European Union, Mr. Cameron said, “I am trying to get for Britain the things that we need, and obviously once I have got them I will turn around and make the case for staying in a reformed Europe.”
He also announced that he had ordered a doubling of Britain’s drones to surveil and target Islamic State militants and would strengthen its special forces as Britain tries to help quell the growth of the Islamic State in Syria and Iraq and pursue those who have killed British hostages, like Mohammed Emwazi, known as Jihadi John, who appears to have taken part in the beheadings of at least seven hostages.
Ten aging drones will be replaced by at least 20 modern drones that can be equipped with weaponry. And two British citizens were recently killed by British drone strikes, a controversial act that Mr. Cameron justified on the basis of the danger of an “imminent” terrorist attack.
National defense and security were to be themes of the conference, Mr. Cameron said. To that end, the home secretary, Theresa May, who is considered a possible successor, said more than 30 people suspected of being jihadists have had their British passports permanently revoked since 2013, and 20 others have had their passports seized temporarily to prevent them from traveling to join jihadist groups.
Ms. May also said the government will publish a revised strategy to combat extremism this month. It will include tougher rules for broadcasters and encouragement for universities to do more to fight radicalism, including restricting lectures from so-called hate preachers. Since 2010, Ms. May has banned more than 95 such preachers from entering Britain.
Mr. Cameron’s deputy and the chancellor of the Exchequer, George Osborne, is considered the favorite to succeed him when he steps down, which he has vowed to do before the end of his term in 2020. Mr. Osborne is not particularly popular among voters and is associated with austerity, but is considered Mr. Cameron’s chosen successor. But by announcing his intention so early, Mr. Cameron has condemned himself and the party to continuing speculation about when he might go and who might replace him.
Boris Johnson, popular London mayor and once again a member of Parliament, is also considered a strong possibility, especially if Mr. Cameron loses the vote on an exit from the European Union.