The Prime Minister has said he will resign by October in the wake of the UK's decision to leave the European Union.

In a statement on Friday morning, hours after the result was confirmed, David Cameron said the will of the British people would be respected. But after campaigning strongly to remain, he said he would not be the one to trigger Britain's exit.

An emotional Cameron said the British people had "made a very clear decision to take a different path" to the one he had supported.

"As such I think the country requires fresh leadership to take it in this direction," he said on the steps of Number 10 Downing Street.

Cameron promised to remain as Prime Minister for a few months in an attempt to "steady the ship" as the FTSE 100 stock market fell 7 per cent and the pound plummeted to the lowest level since 1985.

"But I do not think it would be right for me to try to be the captain that steers our country to its next destination.

"This is not a decision I have taken lightly. But I do believe it's in the national interest to have a period of stability and then the new leadership required," he said as his voice cracked.

Cameron said he had fought the campaign "the only way he knew how" and believed "head, heart and soul" it was better for Britain to remain.

But he congratulated the campaign to leave the EU and urged "those on the losing side to help make it work".

Cameron's decision prompted speculation about the future tenure of Chancellor George Osborne, a close friend of the Prime Minister who had been tipped as a future leader.

There was also speculation about the possibility of a snap general election after the new Prime Minister is announced after the summer.