Steedman met his first wife, Ann Taylor, in 1957 during a production of Oklahoma! and they were married in December of that year in Brackley. They have one daughter, Amanda. The marriage ended officially in 1963.
Steedman's second wife was Actress Judy Parfitt, whom he met in 1960 at the Birmingham Rep. They jointly ran Allerway Limited, an artistic creation company. They have a son, David, who was born in 1964.
In addition to film work, his theatre appearances were extensive, including Ray Cooney's comedy Her Royal Highness in the West End of London and he appeared in numerous television productions, including episodes of The Feathered Serpent, The Professionals, Coronation Street, The Avengers, Babylon 5, The Sweeney, Minder and Barry Morse presents Strange But True. He had a recurring role in the British soap opera Crossroads as Dr. Butterworth. He was also a regular in the final two series of BBC sitcom Citizen Smith (1979–80). He holds the distinction of portraying Nazi Gen. Alfred Jodl twice, first in The Death of Adolf Hitler (1973) and later in The Bunker (1981). Following his role in Bill and Ted, he voiced the character of Justin Hammer in the first season of Iron Man.
In his later life he suffered from Alzheimer's disease, which was the ultimate cause of his death on 4 February 2001. He was buried in East London Cemetery, Plaistow, London.
