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Theatre director, writer and actor Jonathan Miller died this morning aged 85, his family said.

Miller, who shot to fame as part of the comedy revue Beyond the Fringe with Peter Cook, Dudley Moore and Alan Bennett, had a lengthy career that took in medicine, broadcasting, books and the theatre.

He was born into an artistic London family and studied medicine at Cambridge where he became part of a glittering generation of performers who honed their skills in student productions.

In the early days he combined stage appearances with work as a hospital doctor in the capital but the success of Beyond the Fringe changed his life forever and he was soon in demand as a theatre director, in both London and New York, and also worked with the BBC presenting arts programmes and adapting plays for television.

His productions were regularly staged by English National Opera - he made around 15 over four decades there - and he also worked at the National Theatre and the Old Vic but always maintained his interest in medicine, continuing to study, and wrote and presented the 1978 BBC series The Body in Question.

A committed atheist, his interests stretched from religion to the history of camouflage, a subject he curated an exhibition on at the Imperial War Museum, as well as the arts and science. In 2013, he unveiled a one man show in Islington of artwork made from bits of scrap metal and wood and two years later his production of King Lear was greeted with five star reviews.

Miller famously loathed being described as a polymath and was once pushed to describe his career, asked what it said on his passport he hesitated before saying: “I think it says theatre director”.

His family said today: “Our father died this morning peacefully at home with his family around him following a long battle with Alzheimer’s.”

A long-term resident of Camden Town, William published a memoir last year detailing life growing up in a bohemian north London house where regular guests including Bennett, the musician George Melly, playwright Michael Frayn and designer Terence Conran who would gather round discussing the issues of the day and putting the world to rights.

Among those paying tribute today was BBC director-general Lord Hall, who said Miller “was a creative genius whose imagination knew no bounds”.