Murphy was born in Pembrokeshire, in Wales. He studied the violin as a child and won a scholarship to the Purcell School, a specialist music school for children in London. There he came into contact with violinist Yehudi Menuhin, who sparked his interest in Indian music early. Murphy went on to London's Guildhall School of Music and Drama, still as a violinist, where he studied with Catherine Mackintosh and the Amadeus String Quartet. He won several prizes and began a career performing across Britain and Europe in orchestral and chamber music. Murphy's switch to conducting was both instantaneous and profound. As he prepared for an orchestral performance, the conductor suddenly fell ill, and Murphy, the only member of the ensemble who happened to have a baton in his instrument case, was drafted as a substitute. He immediately felt that he had found his calling. He won a Welsh Arts Council scholarship for study in the U.S., where he took classes and taught at Wichita State University in Kansas. Murphy became the last student of the pedagogue Léon Barzin, took a master class with Seiji Ozawa at the Tanglewood Music Festival, and, back in Britain, was mentored by Charles Mackerras, serving as his assistant at the English National Opera.
Murphy has conducted many of the leading British orchestras, including the Royal Philharmonic, the London Philharmonic, and the Philharmonia Orchestra, where he led the London premiere of Gustav Holst's tone poem Indra. He also gave the European premiere of Indra with the Residentie Orkest in the Netherlands. Murphy continued his study of Indian music directly with Shankar, and in 2010, he organized the world premiere of Shankar's Symphony with the London Philharmonic, featuring the sitarist's daughter, Anoushka Shankar. After Ravi's death, Murphy completed (assisted by Anoushka and others) Ravi's only opera, Sukanya. He has recorded both works for the London Philharmonic label. Murphy's efforts to create Indian-Western fusions were not restricted to his work with Shankar; he also conceived of the work Samaagam, which was realized by sarod player Amjad Ali Khan and the Scottish Chamber Orchestra. Murphy conceives of his exploration of commonalities between Western and Indian traditions as an ongoing effort, and he has received support from the Arts Council England for his work in this area. ~ James Manheim, Rovi