Saeed Jaffrey in 1973. (ITV/REX Shutterstock)

Saeed Jaffrey, an Indian-born actor whose charm and magnetism were used to memorable effect when he portrayed a loyal foot soldier in “The Man Who Would Be King,” an Indian statesman in “Gandhi” and a pleasure-seeking slumlord in “My Beautiful Laundrette,” died Nov. 14 at a hospital in London. He was 86.

His family, which announced the death, said the cause was a brain hemorrhage.

After a precocious start on radio and stage in India, Mr. Jaffrey settled in New York in the late 1950s with ambitions of conquering Broadway. He found limited success, and his admittedly compulsive womanizing led to the collapse of his first marriage, to actress Madhur Jaffrey. She later became a renowned cookbook author and cooking-show host credited with popularizing Indian cuisine in the West.

Mr. Jaffrey sought a clean start in London, where his resonant voice brought him work on radio, on the West End stage and eventually on television, where he played a trafficker of illegal immigrants in the late 1970s series “Gangsters” and the proprietor of an upscale Indian restaurant in “Tandoori Nights” in the late 1980s.

His breakthrough performance was in “The Man Who Would Be King,” director John Huston’s adaptation of the Rudyard Kipling ad­ven­ture yarn set in the British Raj. Mr. Jaffrey played a Gurkha translator and fixer who helps two British soldiers (Michael Caine and Sean Connery) execute a massive con on a tribal kingdom in an attempt to reap a fortune.

Saeed Jaffrey, left, in “My Beautiful Laundrette.” (Moviestore/REX Shutterstock)

The film proved to be a huge critical and popular success and established Mr. Jaffrey as a bankable commodity.

He followed that performance with a leading role in director Satyajit Ray’s “The Chess Players” (1977) as a chess-obsessed Muslim aristocrat and a supporting part in director Richard Attenborough’s “Gandhi” (1982) as the Indian founding father Sardar Patel. He drew accolades in director Stephen Frears’s “My Beautiful Laundrette” (1985), a sleeper hit in which he played an upwardly mobile but hinky Pakistani businessman in London.

Mr. Jaffrey appeared in many other projects that explored British-Indian relations, including David Lean’s movie adaptation of E.M. Forster’s “A Passage to India” (1984) and the prestigious TV miniseries “The Far Pavilions” and “The Jewel in the Crown.”

Starting in the mid-1980s, Mr. Jaffrey became a staple of dozens of Indian-made films, in which he often was cast as the delightfully naughty uncle. He also returned periodically to English-language productions, including a recurring role as a shop owner on the British TV series “Coronation Street.”

His death prompted an outpouring of tributes in India. In a tweet, Prime Minister Narendra Modi described him as “a multifaceted actor whose flair and versatility will always be remembered.”

Saeed Jaffrey was born in Malerkotla, in India’s Punjab state, on Jan. 8, 1929. He had an itinerant upbringing in northern India, moving often for his father’s work as a public health doctor.

He traced his earliest interest in playacting to his youth. As a schoolboy, he said, he was small and vulnerable to bullies, so he perfected impressions of teachers to gain favor with other students. After studying history at the University of Allahabad in India, he joined All India Radio, which was seeking English-speaking announcers, in 1951.

He displayed an aptitude for scriptwriting and acting on the radio, and also helped form an amateur theater group in New Delhi that presented works by playwrights as varied as William Shakespeare and Tennessee Williams.

His promise led to a Fulbright scholarship in the mid-1950s to study drama at Catholic University in Washington. He was joined by Madhur Bahadur, an Indian actress he soon married and with whom he had three daughters.

They settled in New York, where Mr. Jaffrey won a supporting role on Broadway as the Brahmin professor Godbole in a well-received 1962 adaptation of “A Passage to India” opposite Gladys Cooper and Eric Portman.

In 1980, he married Jennifer Sorrell, a casting agent. Besides his wife, survivors include his daughters, including actress Sakina Jaffrey.

Mr. Jaffrey was not known for a restrained ego. In interviews, he played up his frisky personal life — further amplified in his memoir, “Saeed, An Actor’s Journey” — and could be dismissive of his work in what he called “silly little Bollywood films.” In 1995, he received the Order of the British Empire for his contributions to drama.

It had taken years for Mr. Jaffrey to support himself solely as an actor. At times, he drew cartoons and worked in publicity and advertising. He was a salesman at Harrods when Ingrid Bergman, who appeared with him in a West End play, spotted him at the London department store.

“I didn’t want her to feel sorry for me, so I put on my jacket and tie and acted like a customer,” he told the BBC years later. “Ingrid said, ‘Oh Saeed, how lovely to see you, are you buying up Harrods?’ When in fact, I had about two pounds in my pocket.”