Sheila Steafel, who has died aged 84, was a versatile and bewitching character actor with an outstanding gift for comic timing. As well as being the regular female cast member on the landmark satirical television show The Frost Report (1966-67) – alongside the emerging talents of John Cleese, Ronnie Barker and Ronnie Corbett – she played opposite, “and sometimes against”, in her words, many of the leading TV comedians of the day, including Peter Cook and Dudley Moore (in Not Only … But Also, 1965), Roy Hudd, Tommy Cooper, Spike Milligan and Kenny Everett.

After the success of The Frost Report, a winner of the Golden Rose of Montreux, she was in demand for guest parts in comedy series. Regular roles included Ivy Watkins in the Granada sitcom How’s Your Father (1974-75), the White Lady in all three series of Richard Carpenter’s charming comedy The Ghosts of Motley Hall (1976-78), and the imperious literary agent supporting debut novelist Diane Keen as she starts to overshadow Tim Brooke-Taylor in the sitcom You Must Be the Husband (1987-88).

But while she was a game comic foil on TV, she shone as a stage performer in one-woman shows at the Edinburgh festival and various London theatres. In The Late Sheila Steafel (1981), Steafel Solo (1982), Steafel XPress (1985) and Victoria Plums (1995) she delivered comic songs and monologues supplied by writers including Keith Waterhouse, Barry Cryer, David Nobbs, Andy Hamilton and Dick Vosburgh.

Her features were distinctive, and she deployed them to comedic advantage. Her lidded eyes could be languidly seductive or quizzically innocent, her brows could arch sardonically while her face remained still, and a wry kink in her lips could curl into a feline smile, accentuated by her high cheekbones.

Vocally dextrous but also a fine physical clown, she created Miss Popsy Wopsy, a woozy, klutzy ingenue – a music hall entertainer who was never quite on note and always just behind the beat. She performed the character in her shows and several times on TV in The Good Old Days in the 1970s and 80s. In person she could deliver drawled witticisms and deadpan putdowns, making her a jolly addition to panel shows such as Juke Box Jury, Call My Bluff and Blankety Blank.

Born in Johannesburg, South Africa, Sheila was the younger of two children of Harold, a garage owner from Lancashire, and his wife, Eda (nee Cohen). There was little professional theatre, but Harold directed and performed in amateur productions, particularly of Gilbert and Sullivan, and the young Sheila would watch from the wings. Her mother was a talented pianist and so her childhood was surrounded by drama and music. She also sang at the local synagogue, where both Harold and Eda were involved in directing the choir.

She was educated at Barnato Park school, not far from her home in the middle-class suburb of Berea, and narrowly avoided being expelled for writing a risqué pantomime.

At Witwatersrand University she studied fine art, but abandoned the course to travel to Britain to audition for the Royal Academy of Dramatic Art (Rada) in London in 1953. She did a term at its preparatory academy, but was told she was unusual and would probably have to wait until she was in her 30s and become a character actor. Undeterred, she enrolled instead at the Webber Douglas Academy, where she won the Margaret Rutherford award for comedy.

After graduation and stints in repertory theatre in Blackpool and Lincoln, in 1959 she worked as an usherette at the Players’ theatre, Charing Cross, which presented Victorian music hall shows, and eventually plucked up the courage to ask for an audition. She passed, and while there honed her comedy skills, created Miss Popsy Wopsy and began to get noticed. Her first West End opportunity came in 1961, when she took over the role of Barbara opposite Tom Courtenay in Billy Liar, directed by Lindsay Anderson.

In 1972 she played opposite Robert Morley in How the Other Half Loves at the Lyric theatre, and she was cast as a female Harpo Marx in A Day in Hollywood, A Night in the Ukraine (New End theatre, 1979), at the insistence of Vosburgh, its writer. She won rave reviews.

She was a memorably eccentric, hip-flask swigging Mistress Quickly in an RSC production of The Merry Wives of Windsor (1985), played Meg in the Birthday Party at the Bristol Old Vic (2006) and carried on to the last performance despite needing spinal surgery when playing Mrs Brice in Funny Girl at the Minerva theatre, Chichester (2008).

Her films included Daleks Invasion Earth 2150AD (1966), Quatermass and the Pit (1967) and the rather less earnest Bloodbath at the House of Death (1984), with Everett and Vincent Price, and co-written by Cryer.

On radio she was a regular cast member of the topical comedy show Weekending (1977-82), was to be heard in plays and readings, and performed in her own vehicles Steafel Plus (1982) and Steafel with an S (1984). In later years she made character appearances in popular TV series such as Doctors (with seven different roles between 2005 and 2016) and Holby City (three between 2007 and 2016).

In 1958 she married the actor Harry H Corbett. After their divorce in 1964 she had various relationships but did not marry again. She described their time together, and her career, in her autobiography, When Harry Met Sheila (2010), and also published a series of short anecdotal stories based on real life encounters entitled Bastards (2012).

• Sheila Frances Steafel, actor and comedian, born 26 May 1935; died 23 August 2019