Tewson was born in Hampstead, London. Her father, william, was a professional musician and played the double bass in the BBC Symphony Orchestra; her mother, Kate (née Morley, born 1908), was a nurse, the daughter of Haydn Morley who captained Sheffield Wednesday in the 1890 F.A cup final. After grammar school, Tewson studied at the Royal Academy of Dramatic Art from which she graduated in 1952. She was briefly married to actor Leonard Rossiter; they divorced in 1961.

A regular comedy performer in sketches featuring Ronnie Corbett and Ronnie Barker on David Frost on Sunday and Hark at Barker (1970), she later appeared in Mostly Monkhouse, a BBC Radio Comedy programme with David Jason supporting Bob Monkhouse. She also appeared a few times in Z-Cars (1963–69) and The Charlie Drake Show (1968). Tewson played Edna Hawkins (usually referred to as Mrs H by Shelley) in the first six series of the British sitcom Shelley (1979–82). Later, she played Jane Travers in Ronnie Barker's sitcom Clarence (1988), which he also wrote, and was his last starring television role before his retirement.

Tewson was featured with John Inman in Odd Man Out (1977), an unsuccessful sitcom, where they played half-brother/half-sister roles. She was rumoured to be Inman's cousin, though she has denied this idea in several interviews.

She also appeared in the 1984 children's film Gabrielle and the Doodleman as the characters Mrs. Briggs (Gabrielle's father's housekeeper) and the Fairy Godmother.

Other television appearances were in an episode of Heartbeat ("Closing The Book", 2002) and as the competition judge, Samantha Johnstone, in an episode in the mystery drama Midsomer Murders ("Judgement Day", 2002). Most recently, she was featured in two episodes of Doctors as kleptomaniac, Audrey Wilson, ("Now You See It...", 2009) and as Marjorie Page, a woman in the early stages of Alzheimer's disease ("The Bespectacled Bounder," 2012). Tewson played a nanny in a 30-second commercial for Nabisco Fruit Newtons, first aired in 1997 in the United States. She also played a school Teacher in a Sugar Puffs "I Want My Honey" advert during the late 1980s/early 1990s.

Tewson appeared semi-regularly as Miss Davenport in Last of the Summer Wine (2003–10), a series written by Roy Clarke who also wrote Keeping Up Appearances. She has also appeared in two episodes of the documentary series Comedy Connections, talking about her work in Keeping Up Appearances (2004) and opposite The Two Ronnies (2005). In 2009, she played the role of Iris in the radio drama Leaves in Autumn written by Susan Casanove, produced by the Wireless Theatre Company.

In 2012, Tewson launched her one-woman show Still Keeping Up Appearances? and is on tour across the UK.