Simson began to compete in shot put as a teenager at Thurrock Harriers in Grays, Essex. He won the junior category at the 1984 English Schools Championships, was the intermediate champion in 1986, then succeeded Simon Williams to the under-19s English Schools' title in 1987. He established himself as the top young shot putter of his generation, winning four straight titles at the AAA Junior Championships and three straight AAA Junior Indoor titles. He set national indoor age bests for 16-year-olds in 1987 and 17-year-olds in 1988. In international competition he placed seventh at the 1987 European Athletics Junior Championships before improving to take the bronze medal at the 1989 edition. He was fifth in the shot put at the 1988 World Junior Championships in Athletics. Growing to a height of, Simson established himself at senior level in the 1989 season. That year he was the winner at the AAA Indoor Championships with a throw of. He was also runner-up to Paul Edwards at the UK Athletics Championships and second to Simon Williams at the AAA Championships. He also made his senior international debut, competing at the 1989 European Athletics Indoor Championships where he came in eleventh place. He improved his personal best to in 1990. He began studying in the United States at the University of Florida and competed athletically for their Florida Gators team. He placed third at the NCAA Men's Indoor Track and Field Championship in 1991, throwing a best of. He achieved a new best of in Tallahassee in May and placed in the top five at the Bislett Games and Athletissima meet in Europe that summer. He was over nineteen metres again at the 1991 Summer Universiade held in Sheffield and was the silver medallist behind Soviet Union's Aleksandr Klimenko. He was second to Paul Edwards at both the AAA and UK Championships that year. He missed most of the 1992 season, bar a pair of third-place finishes at the AAA Championships and the 1992 European Athletics U23 Cup. He returned in 1993, starting with a fifth-place finish at the NCAA Indoor meet. His best throw that year was at the Bislett Games in Norway. He resumed his position as runner-up behind Edwards at the UK Championships but managed to defeat his national rival at the AAA Championships, taking his first senior title at the event. The 1994 season marked the peak of Simson's career. He won the Southeastern Conference Championship title for the Florida Gators before being selected to represent England at the 1994 Commonwealth Games. At the games in Victoria, Canada, he excelled with a throw of in the final – a career best. This meant he edged Courtney Ireland into second to win the gold medal. He completed his final year of college in Florida in 1995, with a highlight including a win at the Florida Relays. Simson was the top Briton at the 1996 British Grand Prix, placing third overall with a season's best of. He claimed the second AAA title of his career by beating Shaun Pickering by a margin of 19 cm. He also placed fourth at the London Grand Prix that year. In 1997 his best efforts came indoors. After an indoor career best of in Florida, he won the UK trials to qualify for the 1997 IAAF World Indoor Championships. He failed to follow up on his Commonwealth success, however, and was eliminated in the qualifying rounds of the global tournament. Outdoors he was runner-up at the UK Championships to Shaun Pickering – the contest marked the first time two athletes had thrown over nineteen metres at the competition. This proved to be his last major outing at national level and he retired from professional athletics in 1998.
