He says he will help in his capacity for the next three months but he will not be the prime minister to lead the nation through these times.
“The British people have voted to leave the EU and their will must be respected. The will of the British people is an instruction that must be delivered. There can be no doubt about the result,” Cameron said in a speech on Friday.
“Across the world people have been watching the choice that Britain has made. This will require strong, determined and committed leadership. I am very proud to have been Prime Minister of this country for six years. I have held nothing back.
“I was absolutely clear about my belief that Britain is stronger, safer and better off inside the European Union. And I made clear the referendum was about this and this alone, not the future of any single politician, including myself.
“But the British people have made a very clear decision to take a different path and as such I think the country requires fresh leadership to take it in this direction.
“I will do everthing I can as prime minister to steady the ship over the coming weeks and months. 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.
“There is no need for a precise timetable today. But in my view we should aim to have a new prime minister in place by the start of the Conservative party conference in October.”
POUND FIRMS AFTER CAMERON, CARNEY SPEECH
Immediately after Cameron’s speech, Mark Carney, governor of the Bank of England, gave his speech, which immediately led to an appreciation of the British pound.
Carney said the bank was prepared for the departure of UK from the EU, assuring the country and foreign investors that it will not hesitate to inject £250 billion into the economy to keep it steady if need be.
The British pound was £1 to $1.38 before the speech and closed at £1 to $1.36 by the end of the speech.
Boris Johnson, a Brexit campaigner and member of parliament is already being tipped to replace Cameron in October.