She was born Adrienne Riccoboni in Glasgow, the daughter of Olive Smethurst and an Italian father Luigi Riccoboni (sometimes spelt Reccobini). Her distinctive Auburn hair came from her mother's Lancastrian Mancunian Smethurst family. In the 1930s her father Luigi (known as Louis) ran the Crown Hotel, Callander, Perthshire. She had one brother.

Corri's film debut was in The Romantic Age (1949), which was followed by Jean Renoir's version of The River (1951). Her other film roles included Lara's mother in David Lean's Dr. Zhivago (1965), and Dorothy in Otto Preminger's thriller Bunny Lake Is Missing (also 1965). She also appeared in a number of horror and suspense films until the 1970s including Devil Girl from Mars (1954), The Tell-Tale Heart (1960), A Study in Terror (1965) and Vampire Circus (1972). She also appeared as Therese Duval in Revenge of the Pink Panther (1978). The range and versatility of her acting is shown by appearances in such diverse productions as the science fiction movie Moon Zero Two (1969) where she played opposite the character actor Sam Kydd (Len the barman), and again in a television version of Twelfth Night (1969), directed by John Sichel, as the Countess Olivia, where she played opposite Alec Guinness as Malvolio.

Corri was acquainted with many of the leading figures in the British theatre, including Joe Orton, and he recounts in his diaries how he asked her advice on how best to end his relationship with his lover Kenneth Halliwell. She enjoyed a good relationship with Kubrick, who joked with her that in the surprise visit sequence in A Clockwork Orange that she was cast in "the Debbie Reynolds part", a reference to Reynolds' role in the film Singin' in the Rain (1952). After completing A Clockwork Orange, Corri kept in touch with Kubrick, who complained to her about the Problem he had of losing socks whenever he did the washing, so for Christmas she gave him a pair of bright red socks, a humorous reference to her scene in Orange, where after Alex had finished snipping off her red pyjama suit, she was naked except for a pair of red socks.

Her other television credits include Angelica in Sword of Freedom (1958), Yolanda in The Invisible Man episode "Crisis in the Desert" (1958), a regular role in A Family at War (1971) and You're Only Young Twice (also 1971), a television series created by Jack Trevor Story, as Mena in the Doctor Who story "The Leisure Hive" (1980), as Veronica in Love in a Cold Climate (1980). She guest starred as the mariticidal Liz Newton in the UFO episode "The Square Triangle" (1970) and was in two episodes of Danger Man (US: Secret Agent, both 1965). She was equally at home in the classics of British theater, giving an outstanding performance as Lady Fidget in a BBC Play of the Month, william Wycherley's Restoration comedy The Country Wife (1977) with Helen Mirren.

In the louche atmosphere of the 1960s, when Peers, film stars and Gangsters rubbed shoulders, Corri became acquainted with some of the figures in London's demi-monde, including the bon viveur and much married John Wodehouse, 4th Earl of Kimberley, as well as socialising with other actors and the Kray twins at their El Morocco club, one of the haunts of the Kray's acquaintance the Conservative Politician Robert Boothby, later Lord Boothby, who used the Krays to supply him with rent-boys.

Corri was married to actor Daniel Massey from 1961 until they divorced in 1967. The marriage to Massey proved to be somewhat tempestuous, with Massey describing the relationship in the following terms, "We were agonizingly incompatible but we had an extraordinary physical attraction." Massey envisaged a domestic life for Corri but she realised that she was not suited to being a full-time housewife and after a six-year hiatus she resumed her career as an Actress. Reports that Corri was married earlier to Derek Fowlds are apparently false.

She has had a major stage career, appearing regularly both in London and in the provincial theatres. She appeared in one of the first English performances in 1968 of Come and Go, Samuel Beckett's one-act "dramaticule", in Beckett's coinage, performed at the Royal Festival Hall as part of "a gala entertainment concerning depravity and corruption" (the words coming from the nineteenth-century definition of obscenity), sponsored by the National Council for Civil Liberties and the Defence of Literature and the Arts Society, which raised funds to support publishers being prosecuted for obscenity. It was directed by Deryk Mendel, with Adrienne Corri appearing alongside Marie Kean and Billie Whitelaw in the roles of Flo, Vi, and Ru. The evening included both classical and rock music, and a mixed programme compèred by George Melly. In his entry for Clifford Anthony Smythe in the online Oxford Dictionary of National Biography, John Calder records that "The profit was much less than expected for a sold-out house, as the person who had volunteered to organise the souvenir programme spent too little time finding advertisers as against providing editorial content."

Despite having significant roles in many films, Corri is best known for one of her smaller parts, that of Mrs. Alexander, the wife of the Writer Frank Alexander, in Stanley Kubrick's dystopian film A Clockwork Orange (1971). Though not originally cast in this role, she was brought in after the previous Actress, reported to be Bernadette Milnes, left the film. Corri was offered the role after two actresses had already withdrawn from the film, one of them, according to Malcolm McDowell (Alex in the film), because she found it "too humiliating -– because it involved having to be perched, naked, on Warren Clarke's (playing Dim the Droog) shoulders for weeks on end while Stanley decided which shot he liked the best." Corri had no such qualms about appearing naked, joking to McDowell: "Well, Malcolm, you’re about to find out that I’m a real redhead." Corri earned Kubrick's respect by her willingness to undergo the grueling process of shooting endless takes. She recalled: "For four days I was bashed about by Malcolm (Alex) and he really hit me. One scene was shot 39 times until Malcolm said 'I can't hit her anymore!'"

She was the author of The Search for Gainsborough, a book written in diary form, detailing her efforts to establish the provenance of a painting of David Garrick that she believes to be by a young Thomas Gainsborough. She also wrote a scholarly article in The Burlington Magazine about the portrait and its connection to Gainsborough's very early work, Self Portrait as a Boy c.1739, (the latter can be seen online at the Historical Portraits Image Library). The book displays her wit and erudition, as well as providing the reader with a fund of anecdotes regarding the Actress herself. Corri's researches and her article are discussed in "Tom will be a genius – new landscapes by the young Thomas Gainsborough", the catalogue of an exhibition at Philip Mould Ltd, 4–28 July 2009, with text by Linsay Stainton and Bendor Grosvenor. Corri's claim that the painting was by the young Gainsborough was based on her detailed researches in the archives of the Bank of England, which indicated that significant financial payments were made to Gainsborough while he was still a boy. Following a claim by Corri for the expense incurred restoring and authenticating the picture, the painting was given to her in May 1990, in an out of court of settlement by the Alexandra Theatre in Birmingham, who disputed her valuation and the attribution to Gainsborough.

Corri died at her home in London on 13 March 2016 from coronary artery disease at the age of 85.