Brussels - EU chiefs told Britain to start negotiations to quit the bloc "as soon as possible", after outgoing Prime Minister David Cameron said on Friday he would leave the negotiations to his successor.

"We now expect the United Kingdom government to give effect to this decision of the British people as soon as possible, however painful that process may be," said a joint statement after Britons voted for a Brexit.

"Any delay would unnecessarily prolong uncertainty."

The statement was issued by EU president Donald Tusk, European Commission chief Jean-Claude Juncker, EU Parliament leader Martin Schulz and Dutch premier Mark Rutte, whose country holds the rotating presidency of the bloc, after crisis talks in Brussels.

Cameron announced he would step down to make way for a new leader by October, adding that the new prime minister would be responsible for officially triggering Article 50 of the EU's Lisbon Treaty to start Britain's divorce from the bloc.

But European leaders made it clear they were keen to get the process over with as quickly as possible and wanted Britain to start talks immediately.

"We have rules to deal with this in an orderly way," the joint statement said.

"We stand ready to launch negotiations swiftly with the United Kingdom regarding the terms and conditions of its withdrawal from the European Union."

It added that Britain remained bound by EU law "until it is no longer a member."