Jonathan Miller, a British polymath who restaged theater and opera classics, kicked off a satirical comedy boom with the irreverent revue “Beyond the Fringe” and periodically abandoned the arts to return to his original career as a physician, died Nov. 27 at his home in London. He was 85.

His family announced the death in a statement, saying he had Alzheimer’s disease.

The 6-foot-3 Mr. Miller was a towering, gangling figure in British culture, celebrated as a director, writer and performer on stage and screen; a public intellectual and television pundit; and a photographer, sculptor and author who just happened to be trained as a doctor, specializing in neurology.

Invariably described as a Renaissance man, Mr. Miller preferred terms like “flibbertigibbet,” once telling People magazine, “Things are always best when there has been a careless abandon about them.” He sometimes had a half-dozen productions going on simultaneously across the world, and he often lamented that he was misusing his time — writing too little or taking himself away from the hospital — even as he collected artistic accolades across Europe and the United States.

Overcoming a childhood stammer, he acquired a reputation as one of England’s most hypnotic and quick-witted conversationalists, turning his interviews into stream-of-consciousness conversations about in-flight flatulence (at 35,000 feet, he said, you could neither hear it nor smell it), Marcel Mauss’s theories of natural magic and the politics of Margaret Thatcher, whom he likened to typhoid.

In part, it was Mr. Miller’s wide-ranging interests that pulled him away from medicine. The son of an author and psychiatrist, he had qualified as a doctor but put his medical training on hold to “frisk about on a stage and do silly things,” as he put it.

He had performed with the University of Cambridge’s Footlights theatrical club and, at the suggestion of an Edinburgh International Festival organizer, co-wrote and starred in “Beyond the Fringe,” a four-man comedy revue that premiered in Edinburgh in 1960 and later moved to London and Broadway, running for 667 performances.

The show lampooned 20th-century philosophy, nuclear weapons, British politics, race and ethnicity, and the prolonged death scenes of Shakespeare, with Mr. Miller refusing to die until he finished such melodramatic lines as “now is steel ’twixt gut and bladder interposed.” In another sequence inspired by his Lithuanian-Jewish ancestry, he quipped: “I’m not really a Jew — just Jew-ish, not the whole hog.”

Co-starring Alan Bennett, Peter Cook and Dudley Moore, the revue was credited with spurring a wave of ambitious new British satire, including the magazine Private Eye and the television programs “That Was the Week That Was” and “Monty Python’s Flying Circus.” It also led Mr. Miller to begin directing, as George Devine of the Royal Court Theatre invited him to stage John Osborne’s comedy “Under Plain Cover,” despite having no experience directing plays.

“Oh,” Devine told him, “you’ll pick it up along the way.”

In London, Mr. Miller went on to work at the National Theatre in the early 1970s, serve as artistic director of the Old Vic theater in the late ’80s, and direct television specials and six Shakespeare adaptations for the BBC. He also directed for leading opera companies — including the Royal Opera and English National Opera in London, the Metropolitan Opera in New York and La Scala in Milan — despite being unable to read music.

While medicine occasionally beckoned, leading him to research fellowships at University College London and the University of Sussex, he always returned to the theater, searching for new ways to fuse science and art. His focus, he said, was on the “negligible detail” and “subintentional actions” — pulling an earlobe, running a hand through hair — that kept a work vivid, fresh and passionately alive.

“It is the small details, the most imperceptible things that matter most,” he told the New York Times in 1998, while directing Mozart’s “The Marriage of Figaro” at the Met. The set, he noted with relish, was outfitted with shelves of tools for boot-cleaning, cooking and other humdrum activities that made the characters’ daily lives all the more real.

“We don’t want to talk about the good and the beautiful,” he added, paraphrasing the philosopher J.L. Austin. “We must consider first the dainty and the dumpy.”

Jonathan Wolfe Miller was born in London on July 21, 1934. His father, psychiatrist Emanuel Miller, was also an artist who did portraits of “shell shocked” veterans of World War I; his mother, the former Betty Spiro, was a novelist and biographer of Robert Browning, the poet and playwright.

Mr. Miller later said that he spent much of his childhood with a nanny who beat him with a broom; he sometimes left home to loiter at railroad tracks, recording the serial numbers of passing trains. But by age 16 he had discovered a comic talent for mimicry, including of chickens, entertaining classmates at St. Paul’s School in London.

While there he met Rachel Collett, whom he married in 1956. She survives him, in addition to their three children, Tom, Kate and William Miller.

Mr. Miller’s early directing work included Robert Lowell’s Obie Award-winning play “The Old Glory,” which premiered off-Broadway in 1964 and starred Frank Langella, Lester Rawlins and Roscoe Lee Browne; and “The Merchant of Venice,” which featured Laurence Olivier at the Old Vic in 1970.

For the BBC, Mr. Miller presented the arts show “Monitor” and adapted “Alice in Wonderland” in 1966, incorporating a score by Ravi Shankar and casting his “Fringe” castmates Cook and Bennett as the Mad Hatter and the Mouse. He also directed “Whistle and I’ll Come to You” (1968), based on a haunting ghost story by M.R. James, and created, wrote and presented “The Body in Question” (1978), a survey of medical history that featured the dissection of a cadaver.

By 1974 his focus had shifted to opera, beginning with Alexander Goehr’s “Arden Must Die” for the New Opera Company in London. His best-known productions included a “Mafia” version of Verdi’s “Rigoletto,” set in 1950s New York, and he was similarly daring in adapting Shakespeare’s “Measure for Measure” to Freud’s Vienna, Puccini’s “Tosca” to Mussolini’s Italy and Richard Strauss’s “Der Rosenkavalier” to pre-World War I Europe.

Mr. Miller received a Tony nomination for directing Jack Lemmon in “Long Day’s Journey Into Night” (1986), in which he had the actors overlap their lines to trim the length from four hours to three, and returned to Broadway to direct “King Lear” (2004), starring Christopher Plummer.

By then, he had grown increasingly frustrated by his reception in Britain, where he said that offering up his work to drama critics was like “rolling a Fabergé egg under a pigsty door.” Nonetheless, he was knighted in 2002 by Queen Elizabeth II, for ser­vices to music and the arts, and maintained a relentless pace of work — using found materials to craft sculptures of metal and wood, photographing city scenes (often just the edges of walls), and continuing to direct.

“You do reach a certain age where people assume you to be either dead or senile,” he told the Guardian in 2015, preparing for his eighth production of “King Lear.” “But my skills as a diagnostician are even more considerable now. And directing is nothing if not diagnosis — the close observance of a character for the minute, seemingly irrelevant details that provide the clue as to what is wrong with them.”