In more recent times the actor had parts in the BBC serial Wives and Daughters in 1999 and was in The Royal on ITV as recently as last year.
Former sports commentator Neil Durden-Smith, who knew Carmichael well through their work for the Lord's Taverners cricket-based charity, paid tribute to the actor.
"When I became a trustee in 1976 he had been chairman for two years. He was a marvellous chairman, very caring, hard working, very responsible.
"It's quite unusual for a full-time working actor to be chairman of a pretty big charity."
Asked what made Carmichael popular on screen, Mr Durden-Smith, 76, said: "He had a twinkle in his eye, a wonderful sense of humour, he was marvellously foppish in a theatrical way. You used to wonder what he would say next.
"He had that love of life and love of people; he gathered people around him like other people gather butterflies or postage stamps."
Actress Anne Reid, a star of TV programmes Dinnerladies and Ladies of Letters, said: "He was a delightful man, I was a huge fan when I was young and he was in the Boulting Brothers films.
Ian Carmichael was awarded an OBE in 2003
"He was the most wonderful comedy actor, things like I'm All Right Jack would make you weep with laughter.
"He had great zest for life, and a lot of style. He belonged to an age of elegance."
Carmichael was appointed an OBE in the Queen's Birthday Honours List in 2003.
In 1979, he wrote an autobiography, Will The Real Ian Carmichael ....
Novelist Kate Fenton, 55, is his second wife. His first wife Pym died in 1983.
He also leaves two daughters, five grandchildren and four great-grandchildren.
Keith Richardson, executive producer of The Royal, said Carmichael had filmed a couple of episodes last year which would be seen when the programme returned to the screen.
"He was an absolute joy, terrific and full of life," Mr Richardson added.
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