Born to Scottish immigrant parents, Murray was born and grew up in Durban, South Africa. His father was a motorcycle racer and later prepared racing cars. Murray studied mechanical engineering at Natal Technical College (now Durban University of Technology, which made Murray an Honorary Professor in 2002 and an honorary doctorate in 2011). He built and raced his own car, the IGM Ford, in the South African National Class during 1967 and 1968.
Murray moved to England in 1969, hoping to find a job at Lotus Cars. But Murray was offered a job at Brabham after coincidentally meeting then Brabham designer Ron Tauranac. When Bernie Ecclestone took over the Brabham team, he appointed Murray Chief Designer. There Murray designed many Grand Prix cars, some of which were World Championship Grand Prix winners. These designs include the extraordinary BT46B, also known as "the Brabham fan car", as well as the World Championship winning BT49 and BT52. Murray developed a reputation for an innovative approach to design, applied not only to car concepts and details but also to race strategy.
Between 1973 and 1985 Murray’s Brabhams scored 22 Grand Prix wins, finished 2nd in the Constructors' Championship in 1975 and 1981, and gave Nelson Piquet Drivers’ Championships in 1981 and 1983. For the 1986 season, Murray designed the radical and highly ambitious lowline Brabham BT55 in an effort to increase downforce without adding excessive drag by lowering overall ride height. The car however was not a success, and the year proved disastrous for Brabham, with the team's 1985 car, the Brabham BT54 called into use for the British Grand Prix in a drastic effort to get results.
Despite the BT55's problems and lack of results Murray remained convinced that his design was correct. During 1986 it was discovered the car's main problem was actually the BMW engine which in the lowline design had to be turned to an angle of 18° from horizontal. This caused oil surge in the corners and also had the effect of harming the engine's already poor throttle response. While the car had better downforce in the corners than its predecessor and was one of the fastest in a straight line, the engine problems saw to it that the car was only competitive on the fast circuits of the year such as Hockenheim, the Österreichring and Monza. In a late 1986 season interview, Murray stated that he believed the lowline concept would work better if mated to a more compact V6 such as the Honda or TAG-Porsche engines, rather than a taller Straight-4 like the BMW. A further noteworthy aspect was the inconsistent Pirelli race tyres which had also hampered the team's 1985 season.
After leaving Brabham, Murray joined McLaren as Technical Director. Learning from his low-line Brabham experience, Murray played a small part in the design team, headed by Steve Nichols, which produced the 1988 Honda-powered McLaren MP4/4 which won 15 of the 16 Grands Prix, and gave Ayrton Senna his first Drivers' Championship. In the Constructors' Championship McLaren's points score of 199 was (at that time) an all-time high. Murray also played a small part in the design of the 1989 MP4/5 and 1990 MP4/5B along with Nichols and Neil Oatley. The MP4/5 and MP4/5B also won the driver's and constructor's championships in both years. Over the period 1988–91 the McLaren team won four consecutive Constructors' and Drivers' Championships: Alain Prost won the Drivers' Championship in 1989, Senna won further Drivers' Championships in 1990 and 1991.
In July 2007 the Gordon Murray Design consultancy was established, and released initial details regarding its upcoming T.25 (Type 25) prototype city car along with mention of a future lightweight, economical supercar project. The T25 will be smaller than a Smart Fortwo.
In November 2009 Gordon Murray Design and Zytek Automotive announced plans to develop an electric-powered version, the T.27.
On 17 November 2008 Gordon Murray won the ‘Idea of the Year’ accolade at Autocar magazine’s annual awards ceremony for the manufacturing process proposed for the T.25.
The car, dubbed T27, will be the product of a partnership between Murray’s company and British technology company Zytek, which will build the powertrain.
In 1981, Murray was involved in improvements for Midas Cars.
Murray also independently designed the Rocket, an ultra-lightweight, open cockpit roadster powered by a 1-litre motorcycle engine, which has an appearance similar to that of a 60's era Grand Prix car. Looking like a pure single-seater, it actually could accommodate a passenger in tandem with the driver. This seat was located beneath a removable cover. The Rocket was built by former racing driver Chris Craft at the Light Car Company.
Murray is also collaborating with TVR to design the upcoming TVR models scheduled for release in 2017.
Murray agreed to sit for sculptor Jon Edgar in 2009 as part of his Environment Series of terracotta heads, on the strength of his developing vision for small car design.