Green was born in Bethnal Green, London. He first played in a band called Bobby Dennis and the Dominoes, which performed pop chart covers and rock 'n' roll standards, including Shadows covers. He later stated that Hank Marvin was his guitar hero and he played the Shadows song Midnight on the 1996 tribute album "Twang." He went on to join rhythm and blues outfit the Muskrats, then a band called The Tridents in which he played bass. In 1966, Green played lead guitar in Peter Bardens' band "Peter B's Looners", where he met drummer Mick Fleetwood. It was with Peter B's Looners that he made his recording début with the single "If You Wanna Be Happy" with "Jodrell Blues" as a B-side. His recording of "If You Wanna Be Happy" was an instrumental cover of a song by Jimmy Soul.