Miles was born in Sutton Coldfield, then in Warwickshire, and left school at fifteen to work as an apprentice at Wolseley Motors, where he received training in vehicle construction. After racing motorcycles in his youth, he joined the British Army during the Second World War, serving initially as a driving instructor in the Territorial Army before becoming an armament artificer. On 1 October 1942 he was among the founding members of the Royal Electrical and Mechanical Engineers (REME). He landed in Normandy on 15 June 1944 and served in North West Europe through to the end of the war, reaching the rank of staff sergeant. He served as a tank commander, and the experience deepened his passion for high-performance engineering. He was discharged in April 1946.
After the war Miles raced Bugattis, Alfa Romeos, and Alvises before emigrating to the United States in 1952, settling in Los Angeles as a service manager for the Southern California MG distributor. In 1953 he won 14 consecutive SCCA victories in an MG-based special of his own design. By 1955 he had built a second special, called the "Flying Shingle," which was highly competitive in the SCCA F modified class on the West Coast.
Miles described himself primarily as a mechanic — "Driving is a hobby, a relaxation for me, like golfing is to others" — but his driving ability was evident to everyone who raced against him. He was sometimes called the "Stirling Moss of the West Coast" and was noted for his courtesy on track. With a strong Brummie accent and a sardonic sense of humour, he was affectionately known to his American crew as "Teddy Teabag" for his tea drinking habits.
Miles became a central member of the Shelby Cobra race team in the early 1960s and was appointed chief test driver of Shelby American in 1963. He played a major role in developing the racing versions of the Shelby Cobra 289, the Daytona Coupe, the 427 Cobra, and ultimately the Ford GT — the GT40 — that would define his legacy.
In 1965 Miles shared a Ford GT Mk II with Bruce McLaren at the 24 Hours of Le Mans but retired with gearbox trouble. Earlier that year he had finished second at the 12 Hours of Sebring with McLaren and won the Daytona 2000 km with Lloyd Ruby.
In 1966 Miles achieved what should have been the peak of his career. He won the 24 Hours of Daytona with Lloyd Ruby and the 12 Hours of Sebring, putting him in position for an extraordinary clean sweep of American endurance racing's three major events. At Le Mans, sharing the drive with Denny Hulme in the number one car, Miles was leading comfortably when Ford executives instructed him to slow on the final lap so that three Ford cars could cross the finish line together for a publicity photograph. Miles complied. When the two leading Fords crossed the line nearly simultaneously, race officials declared victory for the car driven by Bruce McLaren and Chris Amon on the grounds that, having started from a position further back on the grid, they had covered marginally greater distance during the race. Miles was classified second, denied what would have been one of the most remarkable individual achievements in endurance racing history.
Just two months after Le Mans, on 17 August 1966, Miles was testing the Ford J-car — the intended successor to the GT40 Mk II — at Riverside International Raceway in California. The J-car featured a Kammback aerodynamic rear section and honeycomb panel construction, but the design was unproven at high speed. After almost a day of testing, as Miles approached the end of Riverside's one-mile downhill back straight at an estimated speed of over 200 miles per hour, the car suddenly flipped and caught fire, breaking apart and ejecting Miles, who was killed instantly.
The aerodynamics of the J-car were subsequently revised to address the rear-end lift that had caused the accident — a problem later encountered by other manufacturers. Ford installed roll cages similar to NASCAR competition standards in future versions. The significantly revised car, renamed the Ford Mk IV, won both races it entered in 1967: the Sebring 12 Hours and the 24 Hours of Le Mans.
Miles was posthumously inducted into the Motorsports Hall of Fame of America in 2001 and the West Coast Stock Car Hall of Fame in 2020. He is interred at the Abbey of the Psalms Mausoleum of the Hollywood Forever Cemetery in Hollywood, California. His son Peter, who was almost sixteen when he witnessed his father's death trackside, later had a long career in motorsport engineering and management.