Cameron said the UK economy was “fundamentally strong” and “the will of the British people must be respected.”
But the leave vote sent shock waves through the Stock Market as house builders saw 40% wiped off their value.
Cameron said: “I think the country needs fresh leadership.
“I do not think it will be right for me to be the captain to steer the country to its next destination.”
He said a new prime minister will be in place by the start of October.