The statement released on behalf of her family said: “We are deeply saddened to announce that Dame Penelope Keith died peacefully whilst living with cancer at her home in Surrey where she had lived for more than 50 years.
“The family is grateful for the care and support she received throughout her treatments, and ask that their privacy be respected at this time.”
In her tribute, Kendal said: “I am deeply saddened to hear of my friend Penelope’s death.
“The shows I worked on with her were such special times in our lives and demonstrated her comic genius.
“My heart goes out to her beloved Rodney at this time, theirs was a great love story and partnership. She was a joy to know and work with, and she will be much missed.”
Others paying tribute included comedian and presenter Sue Perkins, who praised her on Instagram for having been the “creator of some of the greatest sit com characters of all time”.
Broadcaster Gyles Brandreth remembered Dame Penelope as “such a special lady – a wonderful actress, a real friend, so funny, so generous with the time she gave to good causes”. He added: “Hers was indeed a good life.”
Former culture secretary Sir Jeremy Hunt posted: “Incredibly sad to hear of the passing of Dame Penelope Keith CBE. She was a neighbour and friend where she was dearly loved by all who knew her in Milford.
“She helped Britain laugh at itself, one of our best national qualities, and brought happiness to millions. RIP dear Penny.”
The actress followed that by playing aristocrat Audrey, who was forced to sell her country estate following the death of her husband in To the Manor Born.
The last episode of the first series in 1979 received almost 24 million viewers – the highest audience for any non-live event on British TV in the 70s.
Dame Penelope won another Bafta TV award soon after, this time for best actress for The Norman Conquests and Saving It For Albie.
Her other sitcom credits in the 1980s and 90s included Executive Stress, set in a publishing house; No Job for a Lady, playing a Labour MP; Moving, about a couple selling their house; Law and Disorder, in which she played a barrister; and Next of Kin, which saw children move in with their grandparents.
The much-loved actress succeeded Laurence Olivier as president of the Actors’ Benevolent Fund after his death in 1989.
This century, working largely in theatre, she played Madame Arcati in a 2004 production of Blithe Spirit and Lady Bracknell in a 2007 version of The Importance of Being Earnest.
The actress was a made a dame in 2014 for services to the arts and charity.
London’s West End theatres will dim their lights in her memory on Wednesday.
Claire Walker, co-chief executive of the Society of London Theatre and UK Theatre, said: “We are proud to come together as an industry and honour the life and extraordinarily prolific career of Dame Penelope Keith, who will undoubtedly be remembered for many years to come as one of this country’s most venerated actors.
“We offer condolences to her loved ones and all who knew her.”
A “classic episode” of The Good Life will be shown on BBC Two at 19:00 BST on Monday in tribute, the BBC said.
The BBC’s director of comedy Jon Petrie described Dame Penelope as “one of the defining figures of British television comedy”.
“Her iconic performance as Margo in The Good Life remains one of the nation’s most beloved sitcom roles and continues to delight audiences today,” he said.
