He studied at the Royal Scottish Academy of Music, Glasgow, and the Royal College of Music, London, where he studied under Maurice Sons, a pupil of Henryk Wieniawski and leader of the Queen's Hall Orchestra.
During World War II, McCallum led the National Symphony Orchestra and played with the London Studio Players and the BBC's Overseas Music Unit.
After the war, McCallum rejoined Beecham, this time as leader of the Royal Philharmonic Orchestra.
His hands are seen playing the violin for Stewart Granger in an uncredited role in The Magic Bow (1946).
Guitarist Jimmy Page credits McCallum with giving him the idea of playing his guitar with a violin bow according to MTV's Led Zeppelin rockumentary.