Craxton made a name for himself early in his career as an accompanist, touring for two years with
Emma Albani and twelve with
Clara Butt, covering Europe, South Africa, America, Canada, the South Sea Islands, Australia and New Zealand. He also had long associations with
Nellie Melba,
Lionel Tertis,
Jacques Thibaud,
Elena Gerhardt and
John McCormack. In 1919 Craxton became a
professor at the
Royal Academy of Music. He remained there until 1961, although he continued teaching from his studio long into his later years. Some notable students included
Winifred Atwell,
Joyce Howard Barrell,
Susan Bradshaw,
Howard Brown,
Mary Chandler,
Elaine Hugh-Jones,
Peter Katin,
Alexander Kelly,
Denis Matthews,
Noel Mewton-Wood,
Albert Alan Owen,
Patrick Piggott,
Alan Richardson, and Thorunn Tryggvason (later Ashkenazy). Craxton was also an active
composer. His first published work was "Three Pieces for Pianoforte" (1911). Some of his songs were recorded by John McCormack and
Lauritz Melchior. He also collected musical compositions in association with
Alfred Edward Moffat. Working with
Donald Tovey between 1926 and 1931 he completed an edition of the complete
Beethoven piano sonatas which was published by the
Associated Board of the Royal Schools of Music and has remained in print ever since. ==Personal life==