Willcocks was a chorister at Westminster Abbey, and he then studied at the Royal College of Music, and King's College, Cambridge. After holding positions at both Salisbury and Worcester Cathedrals, he was appointed organist of King's College, Cambridge in 1957 a post he held until 1974. He was also the conductor of the London Bach Choir from 1960, and in 1974 he was appointed director of the Royal College of Music. He retired in 1984.