She was particularly closely associated with baroque and early Italian opera and the works of Benjamin Britten. During her career, which spanned the 1950s to the 1980s, she was considered an outstanding singing actress and widely admired for her dramatic intensity, perhaps best represented in her famous portrayal as Dido, the tragic heroine of Berlioz's magnum opus Les Troyens. As a concert performer, Baker was noted for her interpretations of Gustav Mahler and Edward Elgar.
Baker was born in Hatfield, South Yorkshire. In 1956, she made her stage debut with the Oxford University Opera Club as Miss Róza in The Secret. That year, she also made her debut at Glyndebourne. In 1959, she sang Eduige in the Handel Opera Society's Rodelinda; other Handel roles included Ariodante (1964), of which she later made an outstanding recording with Raymond Leppard, and Orlando (1966), which she sang at the Barber Institute, Birmingham.
With the English Opera Group at Aldeburgh, Baker sang Purcell's Dido and Aeneas in 1962, Polly (Britten's version of The Beggar's Opera) and Lucretia. At Glyndebourne she appeared again as Dido (1966) and as Diana/Jupiter (in Francesco Cavalli's La Calisto) and Penelope (in Monteverdi's Il ritorno d'Ulisse in Patria). For Scottish Opera she sang Dorabella, Dido, Octavian, the Composer and the role of Orfeo in Gluck's Orfeo ed Euridice.
In 1966, Baker made her debut as Hermia at the Royal Opera House, Covent Garden, and went on to sing Berlioz's Dido, Kate in Owen Wingrave, Mozart's Vitellia and Idamantes, Walton's Cressida and Gluck's Alceste (1981) there. For the English National Opera, she sang Poppaea, Donizetti's Mary Stuart, Charlotte (Werther) and the title role of Handel's Giulio Cesare.
During this same period she made an equally strong impact on audiences in the concert hall, both in oratorio roles and solo recitals. Among her most notable achievements are her recordings of the Angel in Sir Edward Elgar's The Dream of Gerontius, made with Sir John Barbirolli in December 1964 and Sir Simon Rattle over twenty years later; her performance of Elgar's Sea Pictures, also recorded with Barbirolli, and the world-premiere recording of Ralph Vaughan Williams's Christmas oratorio Hodie, made in 1965 with Sir David Willcocks. In 1975, she premiered Dominick Argento's Pulitzer Prize-winning song cycle, "From the Diary of Virginia Woolf," written for her by the composer. She has also been highly praised for her insightful performances of the Alto Rhapsody and many lieder by Brahms.
In 1982 Baker retired from opera, after singing Mary Stuart at the ENO and Gluck's Orpheus at Glyndebourne. She published a memoir, Full Circle, in 1982. In 1991, Baker was elected Chancellor of the University of York. She held the position until 2004, when she was succeeded by Greg Dyke.