Wood was born in Oxford Street, London, the only child of Henry Joseph Wood and his wife Martha, "née" Morris. Wood senior had started in his family's pawnbroking business, but by the time of his son's birth he was trading as a jeweller, optician and engineering modeller, much sought-after for his model engines. It was a musical household: Wood senior was an amateur cellist and sang as principal tenor in the choir of St Sepulchre-without-Newgate, known as "the musicians' church". His wife played the piano and sang songs from her native Wales. They encouraged their son's interest in music, buying him a Broadwood piano, on which his mother gave him lessons. The young Wood also learned to play the violin and viola.