The son of an army officer, William Markham studied his degree of Doctor of Civil Law at Christ Church, Oxford. Shortly afterwards, he became headmaster at Westminster School, with which he retained close links for the rest of his life. He resigned from Westminster, after eleven years as headmaster, to focus on his interests in the Church. He returned to Christ Church as Dean in 1767, and enjoyed rapid advancement, becoming Bishop of Chester in 1771 and Archbishop of York in 1776. As a result of this latter appointment, he was also made a Privy Councillor. He is buried in Westminster Abbey.