Brussels: EU leaders have given Britain breathing space by accepting it needed time to absorb a shock Brexit vote before triggering a divorce but insisted the crunch move could not wait months.
A humiliated Prime Minister David Cameron came face-to-face with European colleagues for the first time since last week's vote at a Brussels summit which leaders said was "sad" but pragmatic.
Trillions of dollars have been wiped off world markets since Thursday's vote to leave the EU, while the United Kingdom's future has been thrown into doubt after Scotland said it would push for a new independence referendum.
Further shockwaves juddered through British politics as Jeremy Corbyn, leader of the main opposition Labour party, vowed to fight on despite losing a crushing no-confidence vote among his party's lawmakers.
Thousands of people took to the streets of London, which voted overwhelmingly to stay in the EU, to protest against the referendum result, waving EU flags and placards saying: "Stop Brexit".
After hours of talks in Brussels, EU President Donald Tusk said that he understood that time was needed "for the dust to settle" in Britain before the next steps can be taken.
But reflecting wider concerns of a domino effect of other states wanting to leave, European Commission president Jean-Claude Juncker said Britain did not have "months to meditate".
He set a clear timetable for triggering Article 50, the EU treaty clause that begins the two-year withdrawal process, after Cameron's successor takes office in early September.
Juncker said that if the new prime minister was a pro-remain figure, Article 50 should be activated "in two weeks after his appointment" -- but if it was a supporter of the leave campaign, "it should be done the day after his appointment," he added.
The current favourites to take over from Cameron are leading "out" campaigner Boris Johnson and interior minister Theresa May, a low-key backer of EU membership.
Over a dinner of poached veal tenderloin followed by strawberries, a chastened Cameron urged EU leaders to consider reforming rules on freedom of movement, one of the EU's central tenets, to cement a close relationship with Britain post-Brexit.
He said Britain and the EU should "have as close an economic relationship as possible and that the key to staying close is really to look at reform to free movement," a Downing Street source said, speaking on condition of anonymity.
A British government source added that Cameron believed that free movement was "one of the driving factors in people voting to leave".
At a press conference, Cameron insisted he had no regrets about holding the referendum.
Earlier, US President Barack Obama warned against "hysteria" as stock markets and the pound staged a tentative recovery after days of losses that saw sterling slump to a 31-year low.