Billy was born in 1942 in Glasgow to William (an instrument technician) and Mary (a hospital cafeteria worker). Billy attended St. Gerard's Secondary School in Glasgow.
He work as a welder and boiler in the Glasgow shipyards before moving into a career in stand-up comedy and folk singing.
His popularity grew throughout the 70s and 80s, turning him into an international star by the 1990s. He moved into straight acting with a role in Mrs. Brown opposite Judi Dench.
Billy married Iris Pressagh, an interior designer, in 1969, and divorced in 1985. They had two children: Jamie (b. 1969) and Cara (b. 1973). He married a second time to Pamela Stephenson in 1989, a former comedian and now a Psychologist. They have three daughters: Daisy (b. 1983), Amy (b. 1986) and Scarlett Layla (b. 1988).