He is expected on Tuesday to discuss the vote at an EU summit dinner, while the other 27 leaders will gather for the first time without him on Wednesday morning to plan their next moves.
They are likely to stress a willingness to negotiate, but only after London binds itself to a tight two-year exit timetable.
The leaders of France, Germany and Italy met in Berlin on Monday and said Europe needed to respond to its people’s concerns by setting clear goals to improve security, the economy and prospects for young people.
German Chancellor Angela Merkel, who has appeared to take a softer line on Britain’s decision than some European leaders, said she had “neither a brake nor an accelerator” to control events, adding: “We just don’t want an impasse.”
Cameron’s trip comes amid deep political uncertainty in Britain, sparked by Thursday’s EU referendum in which he failed to convince Britons to vote to remain in the EU.
Shortly after the results were announced on Friday, he promised to resign by October – opening the way for a leadership contest within the ruling Conservative Party.
The decision for a Brexit – or British exit – also caused global markets to sink, Sterling to drop to its lowest level in more than three decades, and threw the opposition Labour Party into crisis.
Many expect a general election in the near future, following Cameron’s resignation and several Labour MPs have resigned, citing ineffective leadership by Jeremy Corbyn.
The political, economic and regulatory uncertainty is being felt across the globe at a time when economies are still slowly recovering from the 2008 economic crisis, interest rates are close to zero, and central banks have fewer tools than normal to revive demand if countries enter recession.
“Who’s running Britain?”
On Monday, there was still an air of confusion in Britain regarding leadership and the plan to leave the EU. Cameron ruled out, however, a second referendum on the issue, following calls to hold another vote.
“Who’s running Britain, and what now is the plan? That’s what everyone wanted to know as government ministers arrived at Downing Street, those who had voted to stay and those whose campaigning to leave had been the undoing of David Cameron.
Not one said a word,” said Al Jazeera’s Laurence Lee, reporting from London.
“But the notable absentee from the meeting, Boris Johnson, used his newspaper column to argue in far more conciliatory terms that things may not be so different in the future, in particular that EU citizens in the UK will not have to leave. Even though many Leave voters wanted exactly that. It was quite different to his tone before the vote.”
Johnson, a Conservative politician and former London mayor, had led the Leave campaign.
“I’ve seen a lot of confusion over the weekend about the status of people living in this country – it is absolutely clear that people from other European countries who are living here have their rights protected,” said our correspondent.
“All that people want to see is a system that is fair, impartial and humane to all people coming from around the world. To put it bluntly there currently is no government and no opposition.” – Al Jazeera