Moore returned to England in 1919; his teacher, Hambourg, referred him to his son, Mark Hambourg, for further study, and Moore began to make frequent appearances in England. In 1921 he accepted a recording contract with the EMI company, remaining with them his entire career. Composer, conductor, and pianist Landon Ronald suggested to Moore that he had an exceptional talent as an accompanist and should concentrate on that art. In 1925 eminent tenor John Coates asked Moore to become his permanent accompanist; Moore said he learned the craft of accompanying from his work with Coates. They made their first joint appearances in 1926. Moore soon became sought-after as an accompanist. His impeccable piano technique was characterized by a beautiful, singing legato touch and lovely, very flexible tone color that was partly the result of masterful use of the pedals. Most important, he was highly empathetic to his recital partners' musical personality. Soon, international artists such as Pablo Casals, John McCormack, Hans Hotter, Maria Gerhard, Feodor Chaliapin, and Elisabeth Schumann made sure they could engage Moore when they appeared in England, or even have him with them on tours. It is not an exaggeration to say that Moore's acceptance of an offer to accompany a new artist was a major indication of the newcomer's promise. He was especially known for his song accompaniment and made frequent and memorable appearances and recordings with Dietrich Fischer-Dieskau, Elisabeth Schwarzkopf, Janet Baker, Kathleen Ferrier, and many others. While Moore was a master of the duo-piano sonata repertory, he did not form any permanent duo-piano partnership. He came more and more to concentrate on song recitals and became a master of the repertory. Moore prompted wide exploration of the more neglected songs of Wolf, Schubert, and Richard Strauss, and participated in recordings of virtually all of the literally hundreds of songs by these masters. During World War II Myra Hess, who had founded a series of lunch-time concert in the National Gallery (which had been emptied of its precious artwork as a safeguard against bomb damage), invited Moore to participate by giving illustrated lectures about the art of accompanying. He proved to be a highly engaging lecture personality, somehow projecting devotion to the highest artistic ideals in down-to-earth, unpretentious terms. After the war, he continued lecturing, making highly successful world-wide lecture tours.
He taught master classes in song interpretation. He published a book derived from his lecture material, The Unashamed Accompanist, which is an engaging combination of forthright discussion of interpretation, mixed with autobiographical (even gossipy) material about working with some of the great stars of the classical music world. In addition, he published teaching books on accompanying and interpretation.
Moore retired from the concert stage in 1967, but continued to be active in the recording studio for some years. He is credited with having raised the status of the accompanist to that of a true musical partner with the soloist.