Allen was born in Chard, Somerset, to Dorothy Essex (née Potter) and William Allen.  From the 1950s, Allen appeared in plays by Shakespeare, including for the RSC in both Stratford and London. Her first leading role was that of Katherine (“the shrew”) in The Taming of the Shrew for the Arena Company in Birmingham (1954–56). Among many other Shakespearean roles, she played Hippolyta in A Midsummer Night’s Dream with the Bristol Old Vic Company, a production that moved to London (1957–58), and first appeared with the RSC in 1962. Her later Shakespearean parts included Portia (The Merchant of Venice, Old Vic, London, 1962), Lady Percy (Henry IV, Parts I and II) (RSC, Stratford, 1966), Lady Macduff (Macbeth, RSC, Stratford and London, 1968), Lady Capulet (Romeo and Juliet, RSC, Stratford, 1967), Helen (Troilus and Cressida, RSC, Stratford, 1968), Lady Macbeth (Macbeth, Shaw Theatre, London, 1973) and Goneril (King Lear, Stratford and London, 1974).

Allen appeared with Patrick McGoohan in an episode of Danger Man (“Don’t Nail Him Yet”, 1964), before her guest role in The Prisoner (1967). In the episode “A. B. and C.”, the third episode of the series, Allen was Number 14, a scientist who was one of many who failed in “the Village” to elicit from Number 6 (McGoohan) why he had resigned from a certain organisation. She was pressed by Number 2 (Colin Gordon) to use a new wonder drug and archive film to influence her subject’s dreams, but he was able to manipulate the process and thereby to cause the downfall of Number 2. When not dressed in her subterranean laboratory in a white coat with her hair tied back, Number 14 was seen with flowing hair, walking around the Village in a cape of many colours.

In Bouquet of Barbed Wire, based on a novel by Andrea Newman and described by Philip Purser as a “kinky saga which was much discussed … well made and acted”, Allen’s character was the wife of Peter Manson (Frank Finlay), who had an unhealthy obsession about his married daughter, Prue (Susan Penhaligon). Among many sexual entanglements, Cassie had an affair with Gavin Sorenson (James Aubrey), her own son-in-law.

She also portrayed the Matron Mary Taylor in the television series Shroud for a Nightingale (1984), based on the P.D. James novel.  Her many film credits include The Prince and the Pauper (1962), Children of the Damned (1963), The Alphabet Murders (1965), and Harry Potter and the Goblet of Fire (film) (2005). Allen continued to work into the 21st century, and taught at the Guildford School of Acting.  Allen died in London on 13 October 2011, nine days before her 79th birthday.