Davidson has designed postage stamps for the UK's Royal Mail, including the 1993 "Sherlock Holmes" set, "The Station", in the 2003 "British Pub Signs" set, four of 2010's "Business and Consumer Smilers", "Paralympic Games - Equestrian" in the "Olympyc Games and Paralympic Games 2012" set, the September 2018 "Postal Heritage: Mail by Bike" set and the same year's Christmas stamps.