The Yorkshire-born star who played blue-rinsed battleaxe Mrs Slocombe in the popular sitcom died in the Royal Surrey County Hospital in Guildford.
Her twin sons, Robin and Simon Moore, were at her bedside, according to her agent Joan Reddin, who said: "I represented her for more than 30 years and I was a very close friend as well.
She had had a long illness and various problems but it was very quick in the end. Her twin boys were with her and she faded away. She was a lovely, lovely person and I never had any trouble with her. She was a great professional."
And Frank Thornton, who played Captain Peacock in the show, said: "Mollie, of course, was an excellent comedian. If you can play comedy, you can play anything - you can play tragedy as well. And if you can only play tragedy, you can't play comedy.
"She was a jolly good actress."
Of their on-screen chemistry in the long-running BBC sitcom, he said: "You can't play comedy if you don't get on. It was a wonderful team."
Sugden, who also starred as the fearsome Mrs Hutchinson in The Liver Birds, made her a household name, not least for her talent of bringing a humorous warmth to the most tyrannical of roles.
Born in Keighley, West Yorkshire, in 1922, she went on to study drama at the Guildhall School of Music and Drama in London, where she took three major awards in one year. Despite this promising start, success did not come quickly and she spent many years in repertory up and down the country.
It was in 1956, while she was working for Swansea Rep at the Grand Theatre, earning about £12 a week, that she met her husband, fellow actor William Moore - best-known for his portrayal of the long-suffering husband and father in the comedy Sorry!, which starred Ronnie Corbett.
They married two years later, when she was 35 and he was 39. Robin and Simon were born six years later, just as Sugden was becoming a familiar face on television with hit programmes such as Hugh And I, Please Sir! and The Love Of Ada.
She quickly found her strength was in comedy and she was happiest in comedy dramas.
It was as the formidable Mrs Hutchinson in The Liver Birds that she started to show her true potential. It was a series that was so popular in the late 60s and early 70s that it was revived in the late 90s using the original cast.
She was the star of many other comedies, including Come Back Mrs Noah, That's My Boy and My Husband And I, which she made with her husband.
But it was as the bossy sales lady Betty Slocombe in Are You Being Served? that she was best known. The long-running television comedy was such a hit that a feature film was made based on the series.
In the early 1990s, re-runs of Are You Being Served? transformed both Sugden and co-star John Inman, famous for his catch phrase "I'm free" into cult figures.
Such was her popularity in America that at the age of 71 she was asked to appear in Donizetti's opera La Fille Du Regiment in a non-singing role.