Brexit means Brexit, says Home Secretary Theresa May, who will become Britain's prime minister on Wednesday, according to David Cameron and the . Theresa May says she's humbled and honoured to have been chosen as the Conservative Party's new leader, and in turn the next British Prime Minister. David Cameron says he is 'delighted' there will not be a protracted Conservative leadership contest and will hand in his resignation on Wednesday, paving the . David Cameron has announced he will resign as Britain's Prime Minister on Wednesday evening. Cameron will be succeeded by Theresa May. The home .