Nimmo - a comedy actor and producer who made his name playing ineffectual vicars and upper-class twits - had spent Christmas in a coma after the fall on 2 December, but regained consciousness at the end of that month and was recently reported to be making good progress in hospital.
Nimmo's agent, Barry Burnett, said the actor had developed pneumonia over the past 24 hours and died at about 5pm yesterday. His wife Pat, sons Tim and Piers and daughter Amanda were with him when he died. Mr Burnett said: "It is so sad, it almost spells the end of an era. I think he epitomised the English gentleman. He was a very versatile actor who everybody loved."
Mrs Nimmo and the children kept a vigil at his bedside throughout his illness. The couple were married for 43 years.
Nimmo made his name in the Sixties television adaptation of P G Wodehouse's Bertie Wooster and Blandings Castle novels and was particularly successful in his role as the Rev Mervyn Noote in the television comedy series All Gas and Gaiters. He was also a panellist on the long-running BBC Radio 4 programme Just a Minute, in which players try to speak on a particular topic for 60 seconds without hesitation, deviation or repetition.
Although known best for his acting, he was also a successful author, after-dinner speaker, and theatrical impresario. But a quadruple heart bypass operation a decade ago coincided with a scaling down of his TV appearances.
Nimmo was noted for his interest in odd health tonics - including the drinking of bats' and lizards' blood. He also swore by the use of garlic and when featured on Desert Island Discs chose it as his luxury. At a fundraising dinner for past castaways, he donated a sackful of garlic bulbs to an auction.