Born in South Norwood, South London, Budd became interested in music at an early age and began to play the piano when he was two, initially by ear and then by copying various melodies he heard by listening to the radio. When he was six, two Austrian music experts visited him at home and after various tests, found that he had perfect pitch. In 1953, he made his public concert debut at the London Coliseum. By the age of eight, he could play the Wurlitzer organ and four years later he was appearing on television at the London Palladium. Although widely thought to be a self-taught pianist, he did also receive piano lessons from a lady called Mrs Sax who also lived in Mitcham.