The Leeds born talent was famous for his work on The Morecambe and Wise Show and I'm Sorry I Haven't a Clue.
He wrote for many iconic performer including Tommy Cooper, Les Dawson, Sir Bruce Forsyth and Spike Milligan.
Cryer “died peacefully, in good spirits and with his family around him” on Tuesday afternoon at Northwick Park Hospital in Harrow, north-west London.
During his seven-decade career, he appeared on stage, screen and radio, and wrote jokes for countless household names.
A statement from his family said: “Dad was a talented comedy writer and comedian in a particularly golden vintage. Incidentally he never really liked the terms ‘comedy writer’ or ‘comedian’, instead preferring hack and entertainer, and always thought the term ‘national treasure’ meant he’d just been dug up.
“He was, in his words, arrogant in his humility. He had a gift for friendship (as anyone who still has a landline will testify) and a genius for putting people at their ease. Oh yes, and he made many people laugh. A lot. Over many years.
“Baz was, firstly, a loving husband to Terry for nearly 60 years and a gentle father to Tony, David, Jack, Bob. He was a friend to their partners Jayne, Matt, Garry and Suzannah.
“As a grandfather Ruby, Tom, Evan, Archie, Hope, Martha and Connie all loved him and, more recently, Ruby’s daughter, Isobel, had the good fortune to spend time with him as a great grandfather.”
His family said a funeral will take place in the coming weeks and will be followed later by a “more inclusive” memorial service.
They also asked for messages, photos or videos to be submitted to a book of condolence, details of which will be announced on Twitter.
The family statement continued: “He leaves behind him a life of fun, joy, love and silliness and we’ll all be doing our best to maintain that legacy.
“He regularly told fantastic stories and anecdotes about others – the many brilliant and fascinating people he’d worked with and knew – but as he was loved and admired by so many why don’t we start telling some stories about Baz and his brilliant and mischievous life and career?
“And to end, as Dad would say, ‘Same time tomorrow?”
Broadcaster and author Gyles Brandreth, a close friend of Cryer, was among those paying tribute.
Sharing a photo of them together on Twitter, he said: “Here we are only a few weeks ago. Baz was just the loveliest guy: funny & generous.
“He’d worked with everybody & everybody he worked with liked him. I shall miss his happy company so much – & his regular phone calls: he gave you a gem of a joke with each one.”
He added: “Wherever Barry went he brought laughter with him – even to memorial services. And he went to lots because he’d worked with everyone!
“He was generous about everyone: a great mentor & friend.”
Dame Esther Rantzen paid tribute to Cryer as an “encyclopaedia of humour”.
The TV presenter, who first worked with Cryer in the 1960s, told the PA news agency: “In a way Barry was a genius, but so unassuming that he would be astonished, I think, to be called a genius – but he was.
“His jokes were brilliantly crafted and a constant joy. He would ring his friends up with his latest parrot jokes or with some reflection on what was happening. He was so generous with his wit.”
Cryer was born in Leeds and studied English literature at the University of Leeds.
He had a long-running partnership with Sir David Frost, with their collaborations including The Frost Report on the BBC.
He was also a panellist on BBC Radio 4’s I’m Sorry I Haven’t A Clue for more than four decades.
He wrote for many veterans of British comedy, including Ronnie Barker, Ronnie Corbett, Sir Billy Connolly and Tommy Cooper.
In 2018, he was handed a lifetime achievement award for his comedy career by the British Music Hall Society.
Cryer was made an OBE in 2001 and was also a member of the entertainment charity the Grand Order of Water Rats.
He married his wife Theresa in 1962 and they have four children.
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