The actor died "peacefully at home in London yesterday", her sons Samuel and Joseph said.
"Although dementia forced her retirement from a remarkable acting career of nearly 70 years, she continued to live at home," a statement to the PA news agency said on Tuesday.
"She was watching Fawlty Towers the day before she died.
"Pru was married to Timothy West for 61 years. He died in November 2024.
"She is survived by two sons and one stepdaughter, seven grandchildren and four great-grandchildren.
"We would like to thank all those who gave Pru such wonderful care at the end of her life: her last days were comfortable, contented and surrounded by love."
Her Fawlty Towers character, Sybil, was the long-suffering wife of Basil Fawlty, played by John Cleese, in a BBC show that won the BAFTA for best scripted comedy in 1976.
The year 2025 marked 50 years since the comedy show first appeared on screens.
Scales had been diagnosed with vascular dementia in 2013.
She also played Queen Elizabeth II in Alan Bennett's A Question of Attribution, a role which earned her a BAFTA nomination and, in 1973, Scales teamed up with Ronnie Barker in the series Seven of One, also for the BBC.
Jon Petrie, director of comedy at the BBC, paid tribute, saying: "She was a national treasure whose brilliance as Sybil Fawlty lit up screens and still makes us laugh today."
Her husband Timothy West, who died in November 2024, starred in TV shows such as comedy drama Brass, sitcom Not Going Out and soaps Coronation Street and EastEnders.
In celebration of their diamond anniversary, West penned the memoir Pru And Me: A Love Story, charting the course of their life, including Scales' dementia diagnosis.
Together the couple filmed 10 series of the Channel 4 program Great Canal Journeys, which saw them travel across the UK and other parts of the world exploring different waterways, and the couple also talked openly about Scales' diagnosis.
Their last journey for the program was broadcast in June 2019.
Scales' big career break was starring in the early 1960s sitcom Marriage Lines, and she also featured in many BBC Radio 4 sitcoms.
Her diverse credits ranged from Long Day's Journey Into Night on stage in the West End in 1991, which also starred West, to playing the widow Sarah in the gentle TV and radio comedy After Henry.
She also appeared in films including 1987's The Lonely Passion of Judith Hearne and Consuming Passions, which also starred Vanessa Redgrave and Jonathan Pryce.
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