Moore shared the stage with such blues and rock musicians as B. King, Albert King, John Mayall, Jack Bruce, Albert Collins, George Harrison, and Greg Lake, as well as having a solo career.
Moore grew up on Castleview Road opposite Stormont Parliament Buildings, off the Upper Newtownards Road in east Belfast, as one of five children of Bobby, a promoter, and Winnie, a housewife.
During a relationship in the late 60´s while he was with Skid Row, his eldest daughter, Saoirse was born.
He was married from 1985 to 1993 and had two sons, Jack and Gus.
Since 1997, he was living with his partner, an artist named Jo, and their daughter Lily (b. In 2003, he had bought a five-bedroom detached Edwardian house in Hove, just west of Brighton, Sussex, to be near his sons.