Olsen was born in London and lived with an aunt and uncle after losing both his parents, Patricia and Kenny, at an early age. He attended the Archbishop Tenison's Church of England School in Kennington. After school he joined various junior stage groups and toured with fringe theatrical companies, such as Incubus and Lumiere and Son until late 1976. At this point he immersed himself in the punk rock scene as lead vocalist with the band Swank (alongside future members of the Lurkers, Chelsea, and Cuddly Toys) until returning to theatre in 1978. Later he helped develop the musical production "Up on the Roof", in which he starred in 1987 at London's Donmar and Apollo theatres.