Miller's family says he "died this morning peacefully at home with his family around him following a long battle with Alzheimer's".

"His death is a great loss to our family and to his friends and will leave a huge hole in our lives," the family said on Wednesday.

One of the country's most important and wide-ranging arts figures, Miller had a decades-long career that encompassed theatre, television and opera.

Some of Britain's largest and most respected arts institutions, including the National Theatre, the British Film Institute and the Royal Opera, hurried to pay tribute to his long career.

Born in London in 1934, Miller studied medicine and qualified as a doctor before turning to the arts, spurred by the success of Beyond the Fringe, a satirical revue he created in 1960 with fellow Cambridge University students Dudley Moore, Peter Cook and Alan Bennett.

The show went from London's West End to Broadway and helped launch a wave of irreverent, satirical comedy that included Monty Python's Flying Circus.

It diverted Miller from a planned career in neurology into the arts.

"It was kind of an accident, really," he told the Associated Press in 1981 - and a decision he sometimes said he regretted.

From the early 1960s, Miller directed plays for both stage and television, including a 1970 production of The Merchant of Venice starring Laurence Olivier.

His TV directing work included a psychedelic 1960s adaptation of Alice in Wonderland for the BBC and, later, six Shakespeare plays for the same broadcaster.

In the 1970s - and despite his inability to read music - he moved into opera, working with major companies including Glyndebourne, the Royal Opera and the English National Opera.

His production of Cosi Fan Tutte for the Royal Opera was a staple of the company's repertoire for nearly 20 years, and at the ENO he directed 15 productions including The Marriage of Figaro and The Mikado.

The company said Wednesday that "his 40-year contribution to the success of ENO was immense and his productions are loved by audiences of all ages."

Talkative, witty, sometimes acerbic, Miller also presented television series including The Body in Question - a vivid journey through medical history and the human body - and Atheism: a Rough History of Disbelief, wrote books on subjects ranging from Sigmund Freud to acting and took up sculpting and photography.

He was knighted by Queen Elizabeth II in 2002 for services to music and the arts.

Miller is survived by his wife Rachel, children Tom, William and Kate and several grandchildren.

Australian Associated Press