In 1997, he reached the quarter-finals of the revived News of the World Darts Championship.
At the 2008 UK Open, he defeated Adrian Gray, Steve Maish and Brendan Dolan on the way to the quarter-finals, where he was beaten 5–10 by Vincent van der Voort.
Thompson achieved some notable results on the 2010 PDC Pro Tour, reaching the semi-finals in two events.
In one of those events, in Las Vegas, he defeated Phil Taylor in the quarter-finals before losing to Simon Whitlock.
Thompson iss not a full-time professional darts player – he works for a legal firm in York.