LONDON, June 24 - Britain's David Cameron said he would resign as prime minister by October after Britons voted in a referendum to leave the European Union.

"I do not think it would be right for me to be the captain that steers our country to its next destination," he told reporters outside his Downing Street office. 

Cameron, who choked back tears, gave no detailed timetable but said there should be a new leader by the time his Conservative Party holds its annual conference in October.

"This is not a decision I've taken lightly but I do believe it is in the national interest to have a period of stability and then the new leadership required," he said.

"I think it's right that this new Prime Minister takes the decision about when to trigger article 50 and start the process of leaving the EU."

Britain has voted to leave the European Union, results from Thursday's referendum showed, a stunning repudiation of the nation's elites that deals the biggest blow to the European project of greater unity since World War Two.

World financial markets plunged as complete results showed a near 52-48 percent split for leaving. The vote created the biggest global financial shock since the 2008 economic crisis, this time with interest rates around the world already at or near zero, stripping policymakers of the means to fight it.