Born in London, Murray Stewart read Music at Cambridge University, where he was Organ Scholar at Trinity Hall. His early years were devoted to following a career as an Organist. Following studies in St Albans with Peter Hurford and later with Daniel Roth in Paris on an Arts Council Scholarship, he recorded the complete organ works of Cesar Franck, and works by Vierne for the Danish label, Kontrapunkt.

Since 1988, Murray Stewart has devoted himself exclusively to a conducting career, studying with Harold Gray, Meredith Davies and Sir Charles Mackerras. He has worked with many Orchestras including the Royal Philharmonic Orchestra, the Philharmonia Orchestra, the Bournemouth Symphony Orchestra, the Ulster Orchestra, the City of London Sinfonia, the Bournemouth Sinfonietta, Sinfonia Viva, and  the Orchestra da Camera. Murray Stewart has also worked with the BBC

Concert Orchestra, with whom he has recorded the complete orchestral works of Maurice Durufle. Abroad, he has conducted the Aarhus Symphony Orchestra, the Musici de Praga and a performance of Beethoven's 9th Symphony at the Smetana Hall, Prague, with the Prague Radio Symphony Orchestra.

Murray Stewart is Artistic Director of the London Pro Arte Orchestra and London Pro Arte Baroque. With the former, he has conducted many Premieres, including works by Ropartz, Langlais, Sallinen, Kokkonen, Szymanowski, Howells, Patterson, Brian Chapple, Piers Hellawell, Geoffrey Burgon, Howard Blake, Naji Hakim and Robert Walker, all to critical acclaim.

Murray Stewart is a former Conductor of the Collegium Musicum of London, where he succeeded Laszlo Heltay, Bristol Choral Society, the East London Chorus and Nottingham Harmonic Society. He was also Artistic Director of Finchley Children's Music Group, with whom he gave the British Premiere of Pierre Max Dubois' opera 'Le ruban merveilleux' at Sadlers Wells, and appeared regularly on television. He appears regularly as a Guest Conductor with other distinguished choirs at home and abroad, including the West German Radio Choir, the Danish National Opera Chorus, and the Pamplona Chamber Choir, Spain.

Since early days, Murray Stewart has maintained a strong interest in French repertoire of the late 19th and early 20th centuries. He has recorded two discs of music by Jean Langlais for Koch International. Murray Stewart also made the premiere Recording of Richard Maunder's edition of the Mozart Requiem, in its entirety, and on modern instruments, as well as a Christmas disc for Conifer Classics, which enjoyed great success in the classical charts. He has conducted over 20 Premieres both at home and abroad, including works by Kenneth Leighton and Naji Hakim. Murray Stewart made the premiere recording of the Requiem Mass by the 19th century Spanish composer Mariano Rodriguez de Ledesma, and also conducted the Spanish Premiere of Charpentier's In Honorem Sancti Xaverij Canticum, in concerts in Pamplona and Madrid. He has conducted performances of the Brahms Requiem at the Vendsyssel and Randers Festivals in Denmark. Murray Stewart is now based in Denmark, and works with the Aarhus Bach Society.