Hambourg grew up in a musical environment: her father was pianist Mark Hambourg, and her mother, Dorothea Muir Mackenzie, studied violin with Eugne Ysaêe. The younger Hambourg's first performances, at age 12, were in duo recitals with her father; at 14 they recorded Schumann's Andante and Variations and Liszt's Concerto Path_tique for two pianos.

In the 1930s Hambourg toured Britian with such singers such as Paul Robeson, Lawrence Tibett, and Richard Tauber. She performed at the BBC Proms in 1938, and in Myra Hess's wartime concerts at the National Gallery.

After World War II, she gave up performing to focus on teaching and counseling music students, eventually establishing the Hope Hambourg Musical Trust, which gives grants to gifted children suffering economic hardship.

Hambourg returned to performing in the last few years before her death, recording Liszt's Legende No. 1 ("St. Francoise d'Assise: La Predication aux oiseaux") and Schumann's Phantasie in C, Op. 17, for Arbiter Records.