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, said: “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.”
Comedian Jack Dee, host of I’m Sorry I Haven’t a Clue which Cryer had also featured in and previously hosted, tweeted: “British comedy just lost its greatest curator and archivist. Thoughts are with Terry and all his family. RIP Baz. ‘There was this parrot……..’”
The BBC’s director-general Tim Davie said Cryer was a “uniquely funny, talented and generous person”.
In a statement, Davie said: “He was an incredible comedian and writer. If you heard or saw a great sketch there was always a good chance Barry was behind it. He worked with every major showbiz legend because everyone wanted to work with him.
“Barry will be hugely missed by his many friends at the BBC and the wider public.”
Comedian David Mitchell said he was “so proud” to have known the veteran comic, adding in a tweet: “He was a brilliant man and a bringer of huge joy who never stopped being delighted by comedy. What an amazing life.”
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.
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.