Murray made his stage debut at Stratford-upon-Avon in 1933, and he played such parts as Seyton in "Macbeth", among smaller roles. He later did seasons at the Malvern Festival and at the Birmingham Repertory Theatre, where he played Hamlet. He worked at the Old Vic in London with Laurence Olivier and Tyrone Guthrie. He also played at the Open Air Theatre in Regent's Park, and in the West End. At the Westminster Theatre in 1940 he portrayed the title character in John Drinkwater's "Abraham Lincoln". He was in many of the plays of George Bernard Shaw, and he did later engagements at the Mermaid Theatre in London and at Stratford, Ontario, Canada. His leading roles on television included Svengali. In 1952 he returned to the Old Vic to play King Lear, and toured Europe in that production. Several years later he also played Lear on radio.