His dancing teacher recommended him for a chorus part in the hit 1929 production "The Five O'Clock Girl" at London's Hippodrome Theatre. Not long after, he joined a touring repertory troupe, the Quaints, and embarked for Asia.
By his account, the Quaints were a bizarre cluster of performers. Some actors would forget their lines and cause the company to transition into another play entirely.
John Mills won the Academy Award for best supporting actor in 1971 for his role in "Ryan's Daughter."
In Singapore one night, the lead actor in "Hamlet" got drunk, and at the last minute the cast decided to do a light comedy with Mr. Mills in the lead. Coward, in the audience and expecting to see "Hamlet," delighted when Mr. Mills made a quick entrance on roller skates and proceeded unintentionally to somersault and crash-land on his back.
Back in London, Coward picked Mr. Mills for a secondary lead in his hailed musical drama "Cavalcade" and then "Words and Music."
But Mr. Mills did not want to be typecast as a song-and-dance man. With the help of friend Laurence Olivier, he became a member of the esteemed Old Vic company and performed Shakespeare.
After that experience, he won plaudits in 1939 as the cynical George in a stage production of John Steinbeck's "Of Mice and Men." To give George a New York accent, Mr. Mills sat through 17 screenings of the James Cagney crime drama "Angels With Dirty Faces."
Mr. Mills's movie career was enhanced by British laws spurring domestic film production. His first big contact with American audiences came when he played a fresh-faced pupil in the popular "Goodbye, Mr. Chips" (1939).
He credited Coward with the decision to turn down a long-term Hollywood contract in the early 1930s and work hard in the British theater to mature as a performer. It was a tough call at the time, but Mr. Mills said he was grateful for Coward's advice, which helped him master the difficult character parts that dominated his career for 50 years.
He served briefly in the Royal Engineers during World War II, until a duodenal ulcer resulted in his discharge in 1942, and then returned to the stage.
His presence at home during wartime also led to prominent film roles. After the war, his stature as a film star was assured. Besides "Great Expectations," he played the conscientious mill-town newspaper editor in "So Well Remembered" (1947) and the commander of a submarine imperiled on a routine mission in "Morning Departure" (1950).
He produced two films with mixed results but disliked the work. It reminded him too much of his stultifying days at the corn exchange. "I couldn't show off," he told a reporter. "And there was too much office work."
He went on to play a notorious general who sends soldiers to their slaughter in "Oh! What a Lovely War" (1969) and the British viceroy in "Gandhi" (1982).
He rarely said a bad word about any of his co-stars, who included Peter Sellers and Michael Caine, or such acquaintances as David Niven, Rex Harrison and Frank Sinatra.
He had a special fondness for Vivien Leigh, Olivier's ex-wife and the star of "Gone With the Wind." Mr. Mills, known for a bawdy sense of humor, said Leigh had "the most staggeringly beautiful face in the world" but also a "terribly rude sense of humor. She could be filthy. It was a marvelous combination."
Mr. Mills, whose marriage to actress Aileen Raymond ended in divorce, was renowned for the length and strength of his second marriage, to playwright Mary Hayley Bell. They married in 1941 and renewed their wedding vows in 2001, when she was suffering from Alzheimer's disease and he was mostly blind.
When some wag suggested that the marriage might not last, Mr. Mills said: "The first 60 years are the worst, so we're hoping to push on from here."
Survivors include his wife, their two daughters and a son, Jonathan Mills, a screenwriter.