Thornton died in his sleep in the early hours of Saturday, David Daly announced.
“Frank was a much loved British actor who played mainly comedy roles and is perhaps best known for his role as Captain Peacock in Are You Being Served? and latterly as Truly in Last Of The Summer Wine,” he said.
“Frank is survived by Beryl, his wife of 67 years, daughter Jane and their three grandchildren.”
Thornton was one of the last of the main members of the cast of Are You Being Served?.
The only surviving member now being Nicholas Smith whom starred as Mr Rumbold.
The successful sitcom ran from 1972 to 1985 and often attracted audiences of more than 20 million.
He also went on to appear in its successor series, Grace & Favour.
He specialised in comedy and over the years took roles in many popular TV shows, including Hancock’s Half-Hour, Sykes and Steptoe And Son, as well as movie spin-off Steptoe And Son Ride Again.
Thornton also appeared in a number of racy British movies including No Sex Please, We’re British and Up The Chastity Belt.
Mr Daly said: “I have been Frank’s agent since 1986 and he has been the most wonderful client as well as being a great friend.
“He will be sorely missed.”
In 2001, Thornton was among the cast for the Julian Fellowes-scripted period drama Gosford Park.
His last credit was in the poorly-received British film Run For Your Wife, alongside Richard Briers, who died last month.
Are You Being Served? co-creator Jeremy Lloyd said he was “very sad to hear this news”.
“He was a great friend and consummate performer who was the glue who really held Are You Being Served? together,” he said.
“He will continue to give people enjoyment.”