Much of her theatrical career was spent in Shakespearean plays, appearing at such venues as the Old Vic, the Liverpool Playhouse, and the Westminster Theatre.

Asherson toured with the Old Vic company from 1940 through 1941 in the roles of Kate Hardcastle in She Stoops to Conquer, Maria in Twelfth Night, Nerissa in The Merchant of Venice, and Blanche in King John.

It was at the Westminster Theatre that she gained especially good notices for her appearance in Walter Greenwood's The Cure for Love in 1945 with Robert Donat.

[5] At the Aldwych Theatre, she played Beatrice to Donat's Benedict in Much Ado About Nothing in 1947 and Stella in the first London production of A Streetcar Named Desire in 1949.

Her final film role was as the unnamed old woman in the haunted house thriller The Others (2001), starring Nicole Kidman.

In 1976, she played the tragic Miss Gailey in seven episodes of ATV's epic dramatisation of Arnold Bennett's Clayhanger opposite Janet Suzman and Denis Quilley.

In 1978, she portrayed Mother Ancilla in the Armchair Thriller adaptation of the Antonia Fraser novel Quiet as a Nun, and appeared as Mrs Wainwright in the 1979 TV miniseries A Man Called Intrepid.