Terry left school at 14 with few qualifications but strong ambitions in design, initially working as an office-boy at a theatrical agency. After colleagues were called up for military service, he was promoted to producing promotional material. In 1943 he enlisted in the RAF and served as an instrument maker.
After completing military service, Terry trained as a draughtsman. Contract design work led to a secondment at Aston Martin, where he worked on the DB2/4. In 1955 he began racing a one-off special called the JVT and subsequently designed his own car, which he named the Terrier. He worked briefly for ERA before joining Lotus in 1958, contributing revisions to the Lotus 7, 11, 12, 15, 16, 17, and Elite models.
The Terrier sports car itself was not initially successful, but a partnership with future Formula One engine builder Brian Hart produced an improved MkII version. In 1959 Hart won 18 of 21 races entered in the Terrier, regularly defeating Lotus entries and generating demand for customer cars — an embarrassment that contributed to Terry being dismissed by Lotus. During this same period Terry supplied drawings for the Moorland Special, which formed the basis of the Gemini Mk1 Formula Junior car.
Following his departure from Lotus, Terry was engaged to design chassis for Gilby Engineering, initially for sports car racing and later for Formula One. The Gilby F1 car was tested by Bruce McLaren but was not raced by a top-line driver, and the project ended when Gilby was acquired by a company outside motorsport. Terry's own part-time racing career also came to an end around this time following an accident.
While working on a freelance basis, Terry was invited back to Lotus full-time by Colin Chapman to design a car for the Indianapolis 500. He produced the rear-engined Lotus 29, which Jim Clark drove to a close second place at the 1963 Indianapolis 500. The follow-up Lotus 34 for 1964 qualified from pole position but completed only 47 laps due to tyre and suspension problems. Terry later attributed this to insufficient development resulting from differences with Chapman.
Terry was also involved in the design of the Lotus 33, the car with which Clark won the 1965 Formula One Drivers' World Championship.
For the 1965 Indianapolis 500, Terry was given full design control of the Lotus 38. The car won that year with Clark and finished second again in 1966. However, Terry left Lotus before the 1965 race, having already accepted a role with Dan Gurney's All American Racers to design a Formula One car.
The car Terry designed for Gurney became the Eagle-Weslake V12, which has been widely regarded as one of the most aesthetically striking Formula One designs of its era.
Terry was subsequently hired by Carroll Shelby to design a Can-Am car for 1967, but the project did not reach completion as Terry was based in the UK and could not oversee development in the United States. He then designed a Tasman Series car for BRM, which became the 1968 BRM P126, and thereafter the BRM-engined Mirage M2 for John Wyer — a car that proved effective but whose racing career was delayed by the continued success of Wyer's Ford GT40s.
Terry also designed and built a lightweight spaceframe Ford Escort Mk1 special saloon for Geoff Wood in 1973, known as the LT40 Hart Escort. Powered by a Brian Hart alloy BDA engine with Lucas fuel injection and weighing only 508 kilograms, it was entered in the 1974 British Special Saloon Car Championship. The car later became successful in the hands of Phil Winter and Andrew Grover in 1978 and 1979. It was discovered again in 2017, complete and original in a barn, and subsequently restored to its 1974 specification.
A Formula 5000 design followed, initially conceived as a privateer project but taken up by the Surtees team and used by David Hobbs to finish second in the 1969 US Formula 5000 Championship. The same chassis also formed the basis for the BMW 269 and BMW 270 Formula Two cars in 1969–70.
BRM commissioned Terry to design an F1 chassis around their V12 engine, resulting in the BRM P207, which competed in the 1977 World Championship without scoring any points. This was Terry's last involvement in Formula One design. He continued work on several projects outside the sport and designed the Viking Formula Three car, but was largely retired from active design work after suffering a mild stroke in 1993.
Terry was a keen cyclist and table tennis player. He assisted Classic Team Lotus with restoration matters in his later years. His wife Iris died in 2008. Terry died in August 2014 aged 90, after a short illness.