Watson began his early chess career with much success, winning the World Under-16 Chess Championship in 1979 with a score of 9.5 out of 13. In British domestic chess, he also excelled, claiming the title of British Champion in 1994.
Watson instituted legal proceedings against the British Chess Federation in 1997 for alleged racial discrimination against him and fellow grandmaster Tony Miles, as part of a campaign by the Grandmasters' Association (GMA). Watson asserted that they were not being selected for major national team competitions, such as the Chess Olympiad and the European Team Championship. Ultimately, Watson won the case, and the British Chess Federation was required to pay compensation to both Watson and Miles.
In addition to playing chess, Watson also worked as a bookshop employee, and he later went on to become the manager of the London Chess Centre. His contributions to chess literature include co-authoring the books "Secrets of Grandmaster Play" and "The French Tarrasch".