Rosemary's initial acting career consisted of English repertory theatre productions. In 1948, she performed in 'Kiss and Tell' at Eastbourne and later in 'Black Chiffon' at Penzance.
She first appeared in New York in 'Climate of Eden.' She then moved back to Britain for her first West End performance in 'The Seven Year Itch' at the Aldwych.
Rosemary made her television debut in 1952 with the TV movie 'Tansy Clampett' and then portrayed the iconic Venetian beauty ‘Desdemona’ in the TV movie adaptation of 'Othello' (1955).
She made her big screen debut with the 1954 American-British historical film 'Beau Brummell,' playing ‘Mrs. Maria Anne Fitzherbert,’ the long-time companion of George IV of the United Kingdom.
In 1956, Rosemary played Cressida in Shakespeare's 'Troilus and Cressida,' while in the 1958 musical adaptation of 'A Tale of Two Cities' (based on Charles Dickens' novel), she played the character of ‘Lucie Manette.’
Rosemary won an 'Obie Award' in 1962 for her performance as ‘Lady Teazle’ in the stage adaptation of Richard Brinsley Sheridan's comedy of manners 'The School for Scandal' (1962, 1966-67). She also performed as ‘Virginia’ in 'The Tavern' and appeared as ‘Nina’ in 'The Seagull,’ and won an 'Obie' for both.
Rosemary had a stint with the 'Bristol Old Vic.' and then the 'Old Vic,' for which she twice performed as ‘Ophelia’ from 'Hamlet,' in the opening productions of 'National Theatre Company's (1963) and the 'Royal National Theatre' (1964).
Rosemary has essayed ‘Helena Andreyevna Serebryakov’ (Yelena) in several adaptations of Anton Chekhov's 'Uncle Vanya.' She first appeared as ‘Yelena’ in the 1963 British film adaptation, then in TV movie in 1967, and finally in the stage adaption in 1967.
She essayed the fictional character and the female protagonist ‘Cathy Earnshaw’ from Emily Brontë's novel 'Wuthering Heights' in its stage adaptation and as ‘Violet Robinson’ in the 1965 version of George Bernard Shaw's four-act drama 'Man and Superman,' for which she won an 'Obie.'
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She played the lead role in the 1965 adaptation of French dramatist Jean Giraudoux's 'Judith' and won an 'Obie.'
Rosemary won her next 'Obie' award for her portrayal of the central fictional character ‘Natasha Rostov’ of Leo Tolstoy's novel 'War and Peace.' She received her first 'Tony' award for playing ‘Eleanor of Aquitaine’ in the 1966 original Broadway production of 'The Lion in Winter.' Both the productions were directed by her first husband.
Rosemary appeared as Rex Harrison's on-screen wife, ‘Gabrielle Chandebisse,’ in the 1968 'DeLuxe Color 20th Century Fox' production 'A Flea in Her Ear,' and also reprised the role in the stage adaptation by Georges Feydeau.
She won her second 'Tony' and a 'Drama Desk' award for the 1972 Broadway adaptation of Harold Pinter's 'Old Times' as ‘Anna,’ a character she had originated in 1971 at the 'Aldwych' (a 'Royal Shakespeare Company' production).
In 1973, Rosemary won 'Drama Desk' awards for playing ‘Blanche DuBois’ in the adaptation of Tennessee Williams' 'Pulitzer Prize'-winning play, 'A Streetcar Named Desire,' (staged at Lincoln Center, New York, 1973) and ‘Portia’ in 'The Merchant of Venice.'
Rosemary won a 'Drama Desk Award' and a 'Tony' nomination for her performance as ‘Julie Cavendish’ in the comedy (revival) of 'The Royal Family' on Broadway (1975-1976). She starred as ‘Fanny’ in another revival (September to December 2009) at the 'Samuel J. Friedman Theatre.'
Rosemary portrayed the lead role of the French author ‘George Sand’ in seven episodes of the 1974 'BBC' miniseries 'Notorious Woman' and won a 'Emmy Award' and a 'Golden Globe' nomination.
Rosemary won a 'Golden Globe Award' and an 'Emmy' nomination for her role as ‘Berta Palitz Weiss,’ a talented pianist, in the 1978 'NBC' miniseries 'Holocaust,' starring Meryl Streep. She appeared as ‘Minerva Chisholm’ in the 'CBS' western miniseries 'The Chisholms' (1979-80, 13 episodes).
She played the supporting role of Norfolk –based prominent left-wing historian, ‘Ann Barrington (Harris)’ and the wife of advertising film director ‘Matthew Fox’ (Frank Finlay) in the 1983 British drama film 'The Ploughman's Lunch' that earned her a ‘BAFTA’ nomination.
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Rosemary won a 'Drama Desk Award' and 'Tony' nomination for her performance as ‘Barbara Jackson’ in the 1985 Broadway revival of Hugh Whitemore's 'Pack of Lies.' The following year, she was inducted into the 'American Theatre Hall of Fame.'
Rosemary played the older version of ‘Calypso’ whose younger version was portrayed by her daughter in the 'Channel 4' adaptation of Mary Wesley's novel 'The Camomile Lawn' (1992). They again played young and elderly incarnations of ‘Valerie Sors’ in the 1999 historical drama film 'Sunshine.'
Rosemary earned an 'Oscar' nomination and a 'National Board of Review' award for her supporting role of ‘Rose Robinson Haigh-Wood’ in the 1994 period drama film 'Tom & Viv.' Thereafter she played one of her most famous characters ‘Aunt May Parker’ in 'Spider-Man' (2002) and reprised it subsequently in the second and third sequels as well (2004 and 2007).
Rosemary appeared as the mother of the lead character (by Annette Bening) in the 2004 comedy-drama film 'Being Julia.'
In 2007, she shared the 'Gotham Award' with the cast of the 2007 crime drama thriller feature 'Before the Devil Knows You're Dead' in which she essayed the character ‘Nanette.’ That year, Rosemary was felicitated with the 'North Carolina Award' for fine arts.
Rosemary lent her voice to ‘VALIS’ for the film adaptation of Philip K. Dick's dystopian novel 'Radio Free Ablemuth’ (2010). She portrayed ‘Agathe von Trapp,’ the eldest daughter of Georg von Trapp of the ''Trapp Family Singers'' in 'The von Trapp Family: A Life of Music.'
Rosemary was honored with a 'Lifetime Achievement in the Theatre' in 2019.