In 1956, Baker sang in opera for the first time with the Oxford University Opera Club as Miss Róza in Smetana's "The Secret". That year, she also sing 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 excellent recording with Raymond Leppard, and "Orlando" (1966), which she sang at the Barber Institute, Birmingham.