Trained at the Royal Academy of Music, Muir first worked in the movies on the quota quickies of the 1930s. His big break came when Alexander Korda signed him as musical director on The Rise of Catherine the Great (1934). He went on to conduct Sir William Walton's score for Henry V (1944) and Hamlet (1948), as a part of a long, distinguished career as one of the most distinguished composers and musical directors in British cinema.