[2]: 6  From 1934 to 1939, he worked for Gainsborough Pictures, a British film production company based in Islington, London.

His next two films, The Weaker Sex (1948) and Paper Orchid (1949), were popular but overshadowed by the success of Morning Departure (1950).

[3] Baker worked for three years at Fox where he directed Marilyn Monroe in Don't Bother to Knock (1952) and Robert Ryan in the 3D film noir Inferno (1953).

Baker worked for television during the 1960s and early 1970s, directing shows including The Avengers, The Saint, The Persuaders!, The Human Jungle, The Champions, and Randall and Hopkirk (Deceased).

He continued to work in films, directing, among others, Quatermass and the Pit (1967), The Vampire Lovers (1970) and Scars of Dracula (1970) for Hammer, and Asylum (1972) and The Vault of Horror (1973) for Amicus.

He also directed Bette Davis in the black comedy The Anniversary (1968), and co-directed (with Hong Kong director Chang Cheh) the Hammer-Shaw Brothers Studio collaboration The Legend of the 7 Golden Vampires (1974).