Gascoine began her acting career in theatre in the 1960s and had regular roles at the Dundee Repertory Theatre. She was also an actress in the Downfield Musical Society in Dundee. Her early work also included collaborations with future film and television director Ken Loach.
From 1970 onwards, Gascoine began appearing on television in series such as Z-Cars, General Hospital, Rooms, Dixon of Dock Green, Softly, Softly: Taskforce and Within These Walls. She had a part in the British sex-comedy Confessions of a Pop Performer (1975) and then had a recurring role playing Letty Gaunt in the BBC period drama The Onedin Line (1976–79).
She became better known in 1980 when she took the lead role in the ITV drama series The Gentle Touch, playing Detective Inspector Maggie Forbes. This was the first British television drama that centred on a female police officer, coming several months before the BBC's similarly themed Juliet Bravo. The Gentle Touch was a huge ratings hit in the UK and ran for five series until 1984, though Gascoine continued to play Maggie Forbes in the more action-oriented spin-off series C.A.T.S. Eyes from 1985-87. Following this, she then appeared as Judy Schwartz in the final series of the sitcom Home to Roost (1989–90) opposite John Thaw, and continued to make guest appearances on British television. She also appeared in the film King of the Wind (1990) opposite Richard Harris and Glenda Jackson.
After a high-profile career that had spanned over twenty years on British television, Gascoine and her second husband, actor Alfred Molina, moved to Los Angeles in the 1990s. Since moving there, Gascoine has made appearances on US television in series such as Northern Exposure and Touched by an Angel, as well as performing extensively in theatre. Though she still lives in Los Angeles, she returned to the UK in 2008 to perform at the Edinburgh Festival Fringe in the play Sister Cities at the Gilded Balloon Theatre.
In October 2009, it was announced that Gascoine was joining the BBC One soap opera EastEnders. She was to play the role of Glenda Mitchell, former wife of Archie Mitchell and mother of Ronnie and Roxy, from early 2010. However, during her first day on set, she withdrew from her filming commitments, as she felt that she "lacked the right experience to film such a big continuing drama". The part was re-cast with Glynis Barber.
In the 1990s, Gascoine began a career as a novelist. Her first novel was Addicted (1994), about a successful television actress in her fifties who embarks on a destructive affair with a younger, half-English/half-Spanish actor in his thirties (Gascoine's real-life husband Alfred Molina is an English actor of Italian/Spanish descent and is 16 years her junior). This was followed by her second novel, Lilian (1995), about a woman who begins a love affair when she goes on holiday to California with her best friend.
Her third novel was Just Like A Woman (1997), which details the story of Daisy, a middle-aged woman who is being pressured by her family to have an abortion after she falls pregnant in her fifties.
Gascoine has been married twice. Her first husband was Dundee hotelier Bill Keith, with whom she had two sons. However, the marriage ended in the 1960s. Gascoine was then left to raise her two sons alone and has not seen Keith since they divorced.
In 1982, she met actor Alfred Molina when they were both working in the same theatre production. They later married in Tower Hamlets, London, in 1986.
Gascoine has suffered from clinical depression for most of her life, which she believes stems from her unhappy time in a boarding school as a child.
In 1997, Gascoine was diagnosed with kidney cancer, though the disease was detected early and she made a full recovery.
In June 2013, Gascoine publicly revealed that she has Alzheimer's disease, at a Beverly Hills gala which was set up to raise money to fight the disease. In November 2016 her husband Alfred Molina reported that she was "in a very advanced stage of Alzheimer's", and had been in a specialist care home for over two years.
On 28 April 2020, Gascoine died at a care home in Los Angeles, California, at the age of 83.