He was educated at Westminster School and at Christ Church, Oxford,[4] where he matriculated on 6 June 1738, graduating BA 1742, MA 1745, BCL & DCL 1752.

He was one of the best scholars of his day, and attained to the headship of his old school and college: he served as Headmaster of Westminster 1753–1765, and Dean of Christ Church 1767–1776.

He was for some time a close friend of Edmund Burke, but his strong championship of Warren Hastings caused a breach.

Bishop Markham was also the person who composed the Latin memorial for George Berkeley, the famous philosopher.

[5] In 1759, Markham married Sarah Goddard, the daughter of John Goddard, a wealthy English merchant of Rotterdam, with whom he had six sons and seven daughters: His granddaughter, Laura Markham, the second daughter of his son William, married William Mure, the Scottish scholar and politician who sat in the Parliament of the United Kingdom from 1846 to 1855 as the Conservative MP for Renfrewshire and was Laird of Caldwell in Ayrshire.