Murray trained at the London School of Medicine for Women and finished her course at Durham. She then worked in Scotland before returning to London in 1905. She was a medical officer at the Belgrave Hospital for Children and then anaesthetist at the Chelsea Hospital for Women.
Murray joined the Women's Social and Political Union in 1908, and acted as physician to the militants. She spoke at meetings and rallies, marched in processions, provided first aid at suffragette demonstrations, and looked after Emmeline Pankhurst and other hunger-strikers after their release from prison. She campaigned with other doctors against the forcible feeding of prisoners.
In 1912 she founded the Women's Hospital for Children at 688 Harrow Road with Louisa Garrett Anderson. It provided both health care for working-class children of the area, and gave women doctors their only opportunity to gain clinical experience in paediatrics in London; the hospital's motto was Deeds not Words.
In the First World War she served in France with the Women's Hospital Corps (WHC). Along with her friend and colleague Dr. Louisa Garrett Anderson, she established military hospitals for the French Army in Paris and Wimereux. Their proposals were at first rejected by the British authorities, but eventually the WHC became established at the military hospital in Endell Street, Holborn, London staffed entirely by women, from chief surgeon to orderlies. Their motto Deeds not Words was used for the second time.
She never married and is buried at the Holy Trinity Church with her friend and colleague, Dr. Louisa Garrett Anderson near to their home in Penn, Buckinghamshire. Garrett's tombstone reads "We have been gloriously happy".
- Deeds and Words in the Suffrage Military Hospital in Endell Street at www.pubmedcentral.nih.gov