European Commission chief Jean-Claude Juncker called for rushing Britain out of the door as the bloc grappled with the impending loss of one of the world's top economies, the first defection in its 60-year history.
Cameron announced yesterday he would resign by October and let his successor lead the exit negotiations under Article 50 of the Lisbon Treaty which sets out a two-year time-frame to leave.
"I do not think it would be right for me to try to be the captain that steers our country to its next destination," the outgoing prime minister said as sterling, global stocks and oil prices plummeted.
Moody's cut Britain's credit rating outlook to "negative", warning of the economic threat to the country.
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"I do not understand why the British government needs until October to decide whether to send the divorce letter to Brussels," Juncker told German broadcaster ARD on Friday evening.
"I'd like it immediately," he added.
"It is not an amicable divorce but it was also not an intimate love affair," he said.
Foreign ministers of the six original EU members - Germany, France, Italy, the Netherlands, Belgium and Luxembourg - gathered in Berlin for the first in a series of emergency meetings over the next week triggered by Britain's decision.
The Franco-German axis at the heart of the bloc, which was born out of a determination to forge lasting peace after two world wars, will propose "concrete solutions" to make the EU more effective, French Foreign Minister Jean-Marc Ayrault told AFP.
EU leaders will open a two-day Brussels summit on the crisis on Tuesday.
Britain faced a historic break-up threat, too, as Scotland refused to be willingly dragged out of the 28-nation European Union when more than 60 percent of its people voted to stay in.