Salvadori was born in Dovercourt in England in 1922 to Italian parents. His most successful periods in competition fell at the beginning and the end of his career. He raced for many teams: MG, Alfa Romeo (for which he debuted in 1947), Cooper-Maserati, Aston Martin (winning the 24-hour Le Mans) Lola Climax and, naturally, Maserati.

Thanks to his success in the Sport category with the Maserati A6GCS in the Castle Combe Race (in 1953 and 1954) and at Goodwood the same year, Salvadori was able to make it into the F1 circus at the wheel of a Maserati 250F. He obtained reasonable results in this car and won at Snetterton, but in non-championship races.

In 1959 at the World Championships he drove a Maserati-engined Cooper, coming 6th at Monaco. His withdrawal from Formula 1 came in 1962 and in the Sport category a few years later. For a short period between 1966 and 1967 he was team manager for Cooper-Maserati.