Film, television and audio
Asher was a child actress who appeared in the 1952 film Mandy and the 1955 science fiction film The Quatermass Xperiment. She also played the title role in dramatised versions of Alice in Wonderland and Through the Looking-Glass in 1958 for Argo Records. In 1961 she co-starred in The Greengage Summer, which was released in the United States as Loss of Innocence. She also appeared in the 1962 film and Disney TV programme, The Prince and the Pauper. Her British TV appearances included three episodes (1956–1958) of the ITV series The Adventures of Robin Hood and as a panellist on the BBC's Juke Box Jury.
In July 1962, Asher appeared in an Out of This World episode called "Cold Equations", playing a teenage stowaway on a space ship. Its captain, played by Peter Wyngarde, is ordered to jettison her into space, and she pleads for her life, but has to come to terms with her imminent death. She then dies calmly.
Asher appeared in Roger Corman's The Masque of the Red Death (1964) with Vincent Price, in Alfie opposite Michael Caine in 1966, and in Jerzy Skolimowski's Deep End (1970) with John Moulder Brown.
Having played Alice herself as an 11-year-old child in the audio recordings of Alice in Wonderland and Through the Looking Glass in 1958, Asher played the real Alice's (Alice Liddell) mother, Lorina Liddell, in the 1985 Dennis Potter film Dreamchild alongside Coral Browne (Alice Hargreaves), Ian Holm (Lewis Carroll/Charles Dodgson), Peter Gallagher, and Amelia Shankley (young Alice).
On television, she guest-starred in the play The Stone Tape and in episodes of Wicked Women, Rumpole of the Bailey and the British television comedy series The Goodies, as Celia Ryder in the 1981 Granada Television adaptation of Brideshead Revisited, and later in A Voyage Round My Father opposite Laurence Olivier, The Mistress (1985–87), and as Faith Ashley in Wish Me Luck (three seasons from 1987 to 1989).
In 1994, she portrayed the Doctor Who companion Susan Foreman in a BBC Radio 4 comedy drama Whatever Happened to Susan Foreman? Another notable radio broadcast was in The Further Adventures of Sherlock Holmes in 2002, in the episode "The Peculiar Persecution of Mr John Vincent Harden".
In 2003, she appeared in the revived ITV soap Crossroads in which she played the hotel's owner Angel Sampson. After the soap was axed, Asher apologised to Crossroads fans for the way the 2003 series went.
In 2006, Asher starred in the Richard Fell adaptation of the 1960s science fiction series A for Andromeda, which aired on the British digital television station BBC Four. In 2007, she portrayed the widow Sandra in the Frank Oz film Death at a Funeral. In the same year Asher appeared in the BBC medical drama Holby City as Lady Byrne. In October 2007, she played Andrea Yates in The Sarah Jane Adventures, in the episode "Whatever Happened to Sarah Jane?" Asher co-starred in the 2008 ITV drama series The Palace, filmed in Lithuania; she played Queen Charlotte, mother of King Richard IV.
In August 2008, Asher appeared with other showbusiness personalities in the reality TV talent show-themed television series Maestro, broadcast on BBC Two. From 2009 to 2010, she played Sally in the BBC One comedy series The Old Guys. In 2011, she played Margaret Harker in Waterloo Road.