The younger son of Ferdinand (Frank) Steiner and Lilian Blumberg, his brother was the film actor Leslie Howard, and his sister the casting director Irene Howard. His uncle was the film director Wilfrid Noy. He married the actress Jean Compton Mackenzie (a daughter of the actor Frank Compton) in 1936 and they had a son together, the stage actor Alan Howard.

Arthur appeared in several television programmes such as Whack-O, a school comedy in which he played the hapless assistant headmaster Pettigrew to Jimmy Edwards's headmaster, and he was in the 1959 film version Bottoms Up. He appeared in many films, including American Friends, The Magnificent Seven Deadly Sins, and had the small role of Cavendish in the James Bond film Moonraker.

He is buried in the East London Cemetery.