Simpson began working with his father as a draughtsman at the glass factory in Harworth. He was riding well; although not selected by Great Britain for the amateur world championships, he made the 4,000-metre team pursuit squad for the 1956 Olympics. In mid-September, Simpson competed for two weeks in Eastern Europe against Russian and Italian teams to prepare for the Olympics. The seven-rider contingent began with races in Leningrad, continuing to Moscow before finishing in Sofia. He was nicknamed "the Sparrow" by the Soviet press because of his slender build. The following month he was in Melbourne for the Olympics, where the team qualified for the team-pursuit semi-finals against Italy; they were confident of defeating South Africa and France but lost to Italy, taking the bronze medal. Simpson blamed himself for the loss for pushing too hard on a turn and being unable to recover for the next.