Born in England of Italian parents, Salvadori's racing career began in 1947 with a 2.9-liter Alfa Romeo. He graduated to Formula 1 via a succession of other cars, including a 2-liter sports Maserati which he drove for Sidney Greene's Gilby Engineering team. From 1954 to 56 Roy handled a Maserati 250F owned by Greene, taking a succession of good placings in predominantly non-Championship events before being asked to drive for the works Cooper squad and later the front-engined Aston Martin DBR4 which did not arrive on the scene until 1959. He later drove for the Yeoman Credit team, in whose Cooper he almost won the 1961 US Grand Prix. He was closing on Innes Ireland's victorious Lotus in the closing stages when the Cooper's engine broke. At the end of 1962 he retired from Formula 1 and quit sports car racing a couple of years later. A successful motor trader, he became heavily involved in the Cooper-Maserati squad in 1966-67 as team manager before retiring to Monaco.