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An only child, she taught at a grammar school after graduating with a degree in English from London University. A film version of her 1967 novel Three Into Two Won't Go, with a screenplay by Edna O'Brien, was released in 1969. It stars Rod Steiger and Claire Bloom and was directed by Peter Hall.
Her sixth novel, A Bouquet of Barbed Wire (1969) was adapted by Newman for London Weekend Television in 1976 as a seven part serial. Newman recalled her work in 2010 at the time of its remake: "I never set out to shock, just to tell a story about an imaginary family, but I imagine most people would still disapprove of hitting your pregnant wife and having sex with her mother." The dramatisation was a popular success, its sequel, Another Bouquet, followed in 1977.
Another similar novel Mackenzie was dramatized by the BBC in 1980, and starred Jack Galloway, Lynda Bellingham and a young Tracey Ullman. This was followed by Alexa (BBC, 1982), A Sense of Guilt (BBC, 1990), and An Evil Streak (LWT, 1999), which were also made into television series. In 2001 Newman was the writer for the television drama Pretending to Be Judith.
Other novels have included A Share of the World (1964), The Cage (1966), Alexa (1968), Mirage (1965), A Sense of Guilt, An Evil Streak (1977), and A Gift of Poison. A book of 15 short stories, Triangles, was published in 1990. It was remarked that a frequent theme in Andrea Newman's novels was that with the advent of a baby, the family disintegrates.