Wedderburn finished second in the 3000m steeplechase at the 1982 UK Athletics Championships behind Roger Hackney, and second at the 1983 AAAs Championships behind Colin Reitz. In 1985, he won a silver medal at the World Student Games (Universiade) behind Italy's Franco Boffi. A two-time winner of the AAAs Championship steeplechase title, he won in 1986 (8:34.03) and in 1987 (8:24.78). Wedderburn competed at the 1987 World Championships in Rome, where the top four in each heat were assured of qualifying for the final. He was fifth in heat one, running 8:24.09 (19th overall).