In 1956, she won the second prize in the Kathleen Ferrier Competition; that year also saw her operatic debut as Roza in Smetana's The Secret, in an Oxford University Opera Club performance. In 1962, she first sang with the English Opera Group, as Polly in Benjamin Britten's famous production of The Beggar's Opera at Aldeburgh. She later credited the leading spirits of that group, Britten and tenor Peter Pears, as giving the ensemble and its singers the highest possible standards, as well as raising the reputation of British singers internationally. In 1966, she made her Covent Garden debut as Hermia in Britten's A Midsummer Night's Dream, and her Glyndebourne debut as Purcell's Dido. In 1971, Britten wrote the role of Kate Julian for Baker in his opera Owen Wingrave, written for BBC television.

As her operatic career progressed, Baker focused on pre-Classical and Classical works such as Gluck's Orfeo ed Euridice, Handel's Giulio Cesare, the title role of Gluck's Alceste, Dido in Purcell's Dido and Aeneas, Ottavia in Monteverdi's L'incoronazione di Poppea, and Dorabella in Mozart's Cosi fan tutte. However, she also performed Romantic and twentieth century roles such as Dido in Berlioz's Les Troyens a Carthage; Donizetti's Maria Stuarda; Charlotte in Massenet's Werther; and Octavian in Richard Strauss' Der Rosenkavalier. Much of her recital repertoire was drawn from the standard works of Fauré, Schumann, Schubert, Duparc, Haydn, and Mahler, and the British masters such as Purcell and Elgar; however, she also drew from the works of lesser-known composers, particularly from the pre-classical period, taking special pleasure in bringing their works to public attention. In 1982, she gave her farewell performances as Orfeo in London and at Glyndebourne.