A successful sprinter at university (he broke Olympic gold medalist Wyndham Halswelle's 53-year-old Scottish 300 yards record in 1961), Campbell competed for the Great Britain team in the 200 metres and 4×100 metres relay at the 1964 Olympic Games in Tokyo, and captained the Scotland team at the 1966 British Empire and Commonwealth Games in Kingston, Jamaica. He also captained the Great Britain athletics team in 1965 and 1966, and held the British 100 metres record from 1967 to 1974. At one time he was known as "the fastest white man on the planet", running the 100m in 10.2 seconds twice during 1967. In his first 10.2-second race he beat O. J. Simpson, who was then an aspiring athlete.