Prior to his business life, Palmer was active in Formula One between 1983 and 1989, and drove for Tyrrell, Williams, RAM, and Zakspeed. He won 14 Championship points from 83 starts. He also raced a Group C Porsche in sports car events between 1983 and 1990, winning the 1984 1000 km of Brands Hatch with co-driver Jan Lammers and taking second place at the 1985 24 Hours of Le Mans with co-drivers James Weaver and Richard Lloyd.