Davis was educated at Stowe School. His father, Sammy Davis, had been among the most prominent figures in British motorsport during the interwar years, winning Le Mans in 1927 with Bentley and later serving as sports editor of Autocar magazine. Colin developed his own competition career, initially racing a 500cc Formula 3 Cooper before moving into longer-distance events, with much of his racing managed from Italy.
Davis made his sole World Championship Formula One appearances in 1959, driving a Cooper T51 powered by a Maserati engine entered by Scuderia Centro Sud. At the French Grand Prix at Reims he retired without a classified finish. At the Italian Grand Prix at Monza he was classified eleventh. He also contested a number of non-championship Formula One races during the same period.
Davis's most consequential results came in sports car and endurance competition. At Le Mans in 1958, sharing an OSCA 750S with Alejandro de Tomaso, he finished tenth overall and took the S750 class victory — a significant early result. At the 1960 Nürburgring 1000 km, co-driving a Ferrari 250 GT with Carlo Abate, Davis finished eighth overall and won the GT class. The pair returned to the Nürburgring in 1961 with another Ferrari 250 GT and improved to fourth overall.
Also in 1961, Davis drove solo to fifth place in the Pescara 4-Hours in a 1,600 cc OSCA Sport. The following year at Le Mans he shared a Ferrari 250 GT prepared by Drago with Carlo Abate for Scuderia Serenissima, retiring with propshaft failure. At Sebring in 1962, he shared a Ferrari 250 GT with Fernand Tavano but retired with engine failure.
The peak of Davis's career came at the 1964 Targa Florio, the demanding Sicilian road race across the mountain Piccolo Madonie circuit. Sharing a Porsche 904 GTS with Antonio Pucci, Davis took an outright victory — the 904's combination of light weight and reliable handling suiting the demanding, narrow public roads of the Sicilian interior.
Later in 1964 Davis returned to Le Mans sharing a Porsche 904/8 with Gerhard Mitter, retiring with clutch failure. The same pairing tried again at Le Mans in 1965 in another 904/8, once more retiring with clutch trouble.
Davis's final major endurance result came at Le Mans in 1966. Sharing a Porsche 906/6 LH with Jo Siffert, the pair completed 339 laps to finish fourth overall and win the P2.0 prototype class — a strong conclusion to a racing career that had begun in 500cc Formula 3.
After retiring from racing, Davis emigrated to Cape Town, South Africa, where he worked as a radio broadcaster. He died on 19 December 2012 following a long illness.