The actor, born in Leeds and educated in Hull and Bridlington, had been battling respiratory problems.
Mr Bayldon is believed to have had one brother but no partner or children.
As well as playing the eccentric wizard transplanted from the 11th century to the present day, he was also known for his role as The Crowman in Worzel Gummidge.
However, he reportedly turned down the role of Doctor Who on two occasions.
Gary Bowers, who founded the Catweazle fan club, which has more than 1,500 members, said: “I always loved Catweazle as a child and whole families used to sit around the telly together on Sunday afternoons to watch it.
“It’s such a timeless piece of work that it will never be dated, the only things that have really changed are the motor cars and the telephone boxes.”
Mr Bayldon trained at the Old Vic Theatre School and appeared in several theatrical productions in his youth before moving into film and TV.
Before his children’s roles, he appeared in several films including Casino Royale, a James Bond spoof based on Ian Fleming’s debut 007 novel, as well as King Rat and To Sir, With Love.
In a 2011 interview, Bayldon said he had no regrets about not taking on the role of Doctor Who.
He said: “I’ve never been in love with sci-fi. It doesn’t terribly interest me.
“I turned it down simply because I’d been playing old men and I didn’t want to play any more.
“I didn’t read a script so I never turned an offer down and when I got Catweazle, I thought, ‘That’s why I turned Doctor Who down’. I’ve played the part on audios since and thoroughly enjoyed doing it.”