In 1966, Baker made her first appearance as Hermia at the Royal Opera House, Covent Garden, and went on to sing Berlioz's Dido, Kate in Britten's "Owen Wingrave", Mozart's Vitellia and Idamantes, Cressida in William Walton's "Troilus and Cressida" and the title role in Gluck's "Alceste" (1981) there. For the English National Opera, she sang the title role in Monteverdi's L'incoronazione di Poppea (1971), Charlotte in Massenet's "Werther", and the title roles in Donizetti's "Maria Stuarda" and Handel's "Giulio Cesare".