Murray began his motorsport career competing in rallies and hill-climbs before graduating to circuit racing. He drove an ERA in domestic and European events, later moving to a Maserati 4CLT that gave him access to front-rank Formula racing on the continent. His experience in both sprint and endurance formats informed his later work as a team organiser, and he brought an understanding of what drivers and cars needed under pressure to his management role.
Murray entered the newly formed Formula One World Championship and participated in five championship Grands Prix, making his debut on 13 May 1950. He competed as both an entrant and driver during this period, gaining direct experience of the highest level of single-seater racing in the immediate post-war era. After one World Championship event under the Ecurie Ecosse banner, he stepped back from driving competitively to focus entirely on running the team he had created.
In 1952 Murray founded Ecurie Ecosse — French for "Scottish Stable" — and based the operation at Merchiston Mews in Edinburgh. The team reflected Murray's conviction that Scotland could field a competitive motor racing outfit capable of challenging on the international stage. Ecurie Ecosse initially ran privately entered machinery in domestic and continental events, building its reputation through careful preparation and disciplined management.
The team's association with Jaguar proved transformative. Running the Jaguar D-Type, Ecurie Ecosse entered the Le Mans 24 Hours in 1956 and 1957 and won on both occasions. These victories against works-supported and factory-backed teams underlined the team's technical and organisational competence, and placed a Scottish private entrant at the summit of sports-car racing during its most fiercely contested era. The back-to-back Le Mans wins remain the most celebrated achievement in Scottish motorsport history.
Murray's accomplishments sit across two distinct but connected roles: a competitive racing driver who raced at Formula One level in the championship's inaugural years, and a team founder whose organisational vision delivered consecutive victories at the world's most prestigious endurance race. The combination was unusual for the period, and his willingness to retire from driving in order to build a successful team operation demonstrated a clarity of purpose that distinguished him from many of his contemporaries.
Murray later moved abroad. He was killed in a road accident in the Canary Islands on 5 April 1973, at the age of 63. Ecurie Ecosse continued to race after his death and remains a name that carries strong meaning in Scottish motorsport culture, with revival efforts undertaken in later decades drawing on the identity Murray created.