Keen made his full film debut in 1946 in Riders of the New Forest but soon appeared in better known films for Reed such as: Odd Man Out (1947), The Fallen Idol (1948), and The Third Man (1949). He quickly became one of the busiest character actors, typically doing five films a year. He also continued to perform on stage, for instance as Iachimo in Peter Hall's 1957 production of Cymbeline, and a sadistic Turkish General in Terence Rattigan's controversial Ross (1960).
Keen was cast mainly as establishment figures, including ministers, senior police officers and military figures, though he also appeared in working class roles in Chance of a Lifetime (1950) and Millions Like Us (1943). He often portrayed balding, cold-hearted, and sarcastic executives or lawyers. On television, he was one of the leads in BBC TV's long-running drama about the oil industry, The Troubleshooters, between 1965 and 1972.
He also appeared in such notable films as The Spanish Gardener, Doctor Zhivago, Cromwell, and Born Free, as well as in numerous TV programmes. He even appeared in a leading role in the Hammer Horror Film Taste the Blood of Dracula that starred Christopher Lee, playing a rather sarcastic Victorian/Edwardian gentleman who is one of a circle of three seeking wicked pleasures who betray Dracula. In all, Keen had appeared in 100 films before he retired in 1991.