He was educated at Rugby School, King's College, Cambridge, where he won a choral scholarship, and later graduated from the Royal Academy of Music.
He worked with Mathieson on the soundtrack recording of William Walton's score for Laurence Olivier's Hamlet in 1948.
As a musical director, he worked on such films as Far from the Madding Crowd (1967), Nicholas and Alexandra (1971), Lady Caroline Lamb (1972), Murder on the Orient Express (1974) and Watership Down (1978).
His television work included Life on Earth, Doctor Who and The Forsyte Saga.
Recordings with Dods as conductor include Malcolm Williamson's The Happy Prince on Argo (with the Academy of St. Martin in the Fields), Lionel Bart's Oliver!