Theatre director also had career in medicine and was member of Beyond the Fringe

Sir Jonathan Miller, the writer, theatre and opera director, and member of the Beyond the Fringe comedy team, has died at the age of 85.

In a statement his family said Miller died “peacefully at home following a long battle with Alzheimer’s”.

Although he hated the term “polymath” his contribution to British culture was wide and praised in many fields. Miller rose to prominence in the 1960s as part of the irreverent satirical show Beyond the Fringe, alongside Peter Cook, Dudley Moore and Alan Bennett.

He studied medicine at Cambridge University, qualifying as a doctor in 1959. He combined his early stage appearances with hospital rounds. But he was soon in demand as a theatre director, in London and New York, and also worked with the BBC, presenting cultural programmes and adapting plays for television.

He made his debut as a theatre director in 1962 with a production of John Osborne’s Under Plain Cover. He went on to direct several celebrated Shakespeare productions including the Merchant of Venice at the National Theatre. It described him as a “legendary figure”.

He also directed a series of critically acclaimed operas in a 40-year career that began in the 1970s for the English National Opera. The Guardian described his contemporary production of Così fan tutte for the Royal Opera House in 1995 as “a compelling piece of music theatre, wonderful in its delineation of Mozart’s mix of comedy and psychological pain”. His Don Pasquale in 2004 was hailed by the paper as a “Hogarthian satire of considerable viciousness”.

In 2007 he made a foray into museum curation with an exhibition about camouflage at the Imperial War Museum. Miller who was a committed atheist, also wrote and presented a 2004 series on the history of disbelief. The National Secular Society said it “broke the hegemony of religion on the BBC”.

Miller shared his insights and enthusiasms from his career in the arts and medicine in a number of television documentaries, which he wrote and presented for the BBC. They included the 1978 series the The Body in Question, which led to spin-off popup book; a five-part series on Madness in 1991; a series on directing opera in 1997; and On Reflection, a 1998 documentary on art.

Miller was a lifelong friend of the writer and neuroscientist Oliver Sacks whom he met at St Paul’s School, London. Sacks, who died in 2015, said that without Miller’s inspiration he would never have his bestselling book Awakenings.

Oliver Sacks Fdn. (@OliverSacks) Remembering Jonathan Miller, polymath and lifelong best friend of Oliver Sacks. As Dr. Sacks wrote in ON THE MOVE, if not for Jonathan, Awakenings would never have been published. He was a constant inspiration.https://t.co/21mGmZBfJH pic.twitter.com/6348LmdtkH

Oliver Mears, the director of opera at the Royal Opera House, said: “Jonathan Miller was one of the most important figures in British theatre and opera of the past half century. Combining a supreme intellect with a consistently irreverent perspective, formed from his experiences in both comedy and medicine, Miller shone a unique light on our art form.”

Tony Hall, the BBC’s director general, said Miller was “a creative genius whose imagination knew no bounds ... he brought arts and culture to millions at the BBC”.

Miller is survived by his wife, Rachel, and three children Tom, William and Kate. They said in a statement: “His death is a great loss to our family and to his friends and will leave a huge hole in our lives.”