Attwood made his Formula 1 debut at the Monaco Grand Prix in the 1965 season for the team Reg Parnell Racing on a Lotus 25 - BRM. , He started eight times for Reg Parnell, reaching each with a sixth place at the Grand Prix of Italy and the Grand Prix of Mexico 's best season rankings.
1966 drove Attwood not in Formula 1 in 1967, he started once for Cooper. His best Formula 1 placement reached Attwood in the first of six races for BRM in the 1968 season with a second place at the Grand Prix of Monaco. In the same race, he also drove his only fastest lap.
After each a race for Lotus and one for Williams in the 1969 season ended Attwood his Formula 1 career with a total of 11 championship points.
Richard Attwood won in 1970 together with Hans Herrmann the 24 Hours of Le Mans in a Porsche 917 It was the first overall victory for Porsche in Le Mans - a historic triumph.