As a 16-year-old, in 1953, she danced in a Folies Bergère-style musical revue, "Pardon My French", at the Prince of Wales Theatre, alongside Frankie Howerd and the pianist Winifred Atwell. She first appeared on television as one of the Dougie Squires Dancers on the British television music show Cool for Cats in 1956. She also appeared as a dancer at the London Palladium. and worked in cabaret, clubs and revues in London, and was in Lionel Blair's dance ensemble.
During 1958–59, Stubbs was the "cover girl" of Dairy Box chocolates, produced by Rowntree. She referred to herself as the "Rowntree's Chocolate Girl", when describing a visit she made to the Rowntree's factory in York (where unknown to her, her grandfather had worked).
In 1963, she joined the cast of new charades-based gameshow Don't Say a Word (ITV), a forerunner of Give Us a Clue. Her first screen role was in the Cliff Richard film Summer Holiday (1963). She also appeared in Richard's next film, Wonderful Life (1964). Soon afterward, she made her breakthrough in television comedy, playing Rita, the married daughter of Alf Garnett in the BBC sitcom Till Death Us Do Part (1966–1975). In 1968, as a direct spin-off from the sitcom, she appeared, alongside Warren Mitchell, in a series of television adverts for Findus frozen products.
She also appeared in the short-lived sitcom Till Death... (1981), again playing Rita. She played Rita a third time in a few episodes of the BBC sitcom In Sickness and in Health (1985–1992). During 1970–71, Stubbs teamed again with Cliff Richard to appear each week on his BBC1 TV Series, It's Cliff Richard!. When she did not take part in the next series as it was broadcast shortly after she had a baby, her TV "mother", Dandy Nichols from Till Death Us Do Part, took her place.
Stubbs featured in the Fawlty Towers episode "The Anniversary" in 1979. From 1979 to 1981, she played Aunt Sally in the ITV children's series Worzel Gummidge opposite Jon Pertwee and Barbara Windsor, and was for several years a team captain in the weekly game show Give Us a Clue in the 1980s, reuniting her with Lionel Blair, the other team captain.
She appeared in the shows Midsomer Murders, Heartbeat, Casualty, Keeping Up Appearances, Born and Bred and The Worst Witch. In recent years, Stubbs also appeared in Victoria Wood's We'd Quite Like to Apologise, The Catherine Tate Show, Agatha Christie's Marple, EastEnders, Benidorm and, from 2010, Sherlock as Mrs. Hudson. She appeared in an episode of Call the Midwife in 2015.
Stubbs was on the West End stage in Noël Coward's Star Quality with Penelope Keith in 2001 and Friedrich Schiller's Don Carlos with Derek Jacobi in 2005. Her other theatre credits included La Cage Aux Folles at the Menier Chocolate Factory, Pygmalion at the Theatre Royal, Bath and Old Vic and The Family Reunion at the Donmar Warehouse. She was in the original cast of The Curious Incident of the Dog in the Night-Time at the National Theatre in 2012.
In 2015 she co-presented The Big Painting Challenge on BBC One alongside Richard Bacon.
