Murray was called to the Bar on 23 November 1730, taking a set of chambers at 5 King's Bench Walk. He was introduced to Alexander Pope around this time, and through his friendship met members of the aristocracy, some of whom later became his clients, including Sarah Churchill, Duchess of Marlborough. Pope also taught him oratory, which helped him enormously in court. His first two cases were in the English Court of Sessions in 1733, where he was led by Charles Talbot and opposed by Philip Yorke. The support of Talbot and Yorke allowed him to gain a respectable practice in the Court of Chancery.