Britain must begin exit talks "as soon as possible", European Union leaders said as they battled to shore up the bloc and prevent a contagion of copy-cat referendums pulling it apart.
The country is on course for a high-stakes stand-off with Brussels after leaders in a joint statement said "orderly" talks must begin without delay, "however painful that process may be".
Britain alone can trigger Article 50, the EU's exit clause, but the EU is now prepared to exert intense pressure to kickstart talks. Boris Johnson, the former mayor of London, yesterday claimed there is "no need for haste" in leaving the bloc.
Mr Cameron said it would be up to the new Prime Minister - expected in office by October - to decide when to trigger the clause.
"We are determined to keep our unity as twenty seven," said Donald Tusk, the Polish president of the European Council.
"Uncertainty is the opposite of what we need," said Martin Schulz , the President of the European Parliament said, saying he could not accept "a whole continent is taken hostage because of an internal fight in the Tory party".
Activating Article 50 begins a two-year negotiation period, during which all current rules apply. While that provides stability, it also bars Britain from agreeing simultaneous trade deals.
Angela Merkel, the German Chancellor, appealed for calm yesterday, saying that leaders must avoid "quick and simple conclusions" and must instead "calmly and prudently analyse and evaluate the situation."
She will host talks with Francois Hollande, the French president, Matteo Renzi, the Italian Prime minister, and Donald Tusk, the European Council president, on Monday.
Mr Cameron will join his 27 former counterparts at a summit on Tuesday, but will be excluded from the session on Wednesday.
Mr Cameron will "explain the situation" to his counterparts over dinner, followed by an "exchange of views" with his counterparts, Mr Tusk said in a letter sent last night.
Mr Hollande said it was a "grave test for Europe". He warned: "It always takes less time to undo than to do, to destroy than to build."
Xavier Bertrand, the president of the Calais region, demanded that the Le Touquet agreement that allows British border checks to be conducted on French soil to be abandoned - a move that could result in illegal migrants reaching Britain and setting up camp.
"The English wanted to regain their freedom; they must take back their border," he said.
Mr Schulz said Britons must face "consequences" in order to avoid a "chain reaction" of referendums.
Jean-Claude Juncker, at a press conference to announce the stance, was asked whether it was the "beginning of the end for the European Union." He replied: "No," before walking off stage, to rapturous applause from aides.
But anti-EU radicals also cheered the result yesterday.
Marine Le Pen, the leader of the Front National, said Europe would be "at the heart" of France's presidential election next spring.
"Victory for freedom!" she said. "We now need to hold the same referendum in France and in other EU countries."
In the Netherlands, Geert Wilders, the leader of the anti-Islam Party for Freedom, also called for a plebiscite, which is backed by a majority of Dutch voters
"As quickly as possible the Dutch need to get the opportunity to have their say about Dutch membership of the European Union," he said.
It was also cheered in Italy by Matteo Salvini, the leader of the anti-immigration Northern League party.
Vladimir Putin, the Russian president who has made undermining European unity a key objective, launched a withering attack on Mr Cameron, saying the referendum was "nothing more than overconfidence and a superficial approach to solving fateful decisions for one's country, and Europe as a whole, on the part of the British leadership".
The result showed how voters wanted to stop "feeding and subsidising weaker economies" and showed the population was "dissatisfied with the approach to security questions", he said.
Iran was also jubilant. Brig. Gen. Massoud Jazayeri, a senior commander in the Revolutionary Guard, said it was payback for "years of colonialism and crimes against humanity". An official in President Hassan Rouhani's office said the vote was a "big earthquake" that is part of the EU's "domino" collapse.
Leaders on both sides of the Atlantic attempted to insist that relations would be unaffected by the move, which President Obama had previously said ran against US interests.
The White House said that Britain and the European Union would "remain indispensable partners "and that the special relationship would be "enduring".
Jens Stoltenberg, the Nato secretary general, said Michael Fallon, the defence secretary, had assured him Britain would "continue to contribute" to the alliance. A British battalion is due to be deployed early next year to Estonia as part of a "tripwire" force to deter Russia.
However, Mr Stoltenberg admitted the vote - which could result in the breakup of the UK and the jettisoning of the Trident nuclear deterrence - makes for "a more unpredictable situation".