Her agent Joan Reddin told newspapers Sugden died on Wednesday after a long illness. "She was a lovely, lovely person. She was a great professional," Reddin said.
With her hair highly coiffed and referring frequently to her "pussy," Sugden played the bossy Mrs Slocombe throughout the run of the BBC's innuendo-laden Are You Being Served? between 1972 and 1985.
Re-runs of the show in the United States in the 1990s gained her a new audience overseas.
"She was great fun, a very good actress, very versatile. She could play serious stuff and comedy," said Frank Thornton, who played opposite Sugden in the series as the stuffy floorwalker Captain Peacock.
"It was a very happy show to work on -- you can't play comedy with people you dislike," he told BBC television.
Mark Freeland, head of BBC comedy, said she was one of television's iconic funny women.
"Her daftly enormous purple rinse and never-to-be-forgotten catchphrase are the stuff of comedy legend," he said.
Sugden had also found success in the BBC TV comedy series "The Liver Birds" and played an occasional role as pub landlady Nellie Harvey in the long-running ITV soap opera "Coronation Street."