Thompson entered the BTCC in 1994 in a privately entered Peugeot 405. His performances were strong enough to earn him a factory Vauxhall drive for 1995, when he became the youngest-ever race-winner in the championship, also taking two pole positions before a crash at Knockhill gave him an eye injury that ended his season early.
In 1996 he moved to a new Vauxhall Vectra in a transitional season, taking one victory at Snetterton. For 1997 he joined Honda and developed into a consistent frontrunner, finishing fifth in 1997, third in 1998, and fourth in 1999. He was considered a pre-season title favourite for 2000 but missed two rounds after sustaining a concussion in a heavy backwards accident at Brands Hatch.
When Honda withdrew at the end of 2000, Thompson raced a Vauxhall for Team Egg Sport in 2001, taking four wins and finishing third overall. That form earned him a return to the factory Vauxhall squad for 2002, where he became embroiled in a multi-year battle with teammate Yvan Muller. Thompson won the BTCC title in 2002 and again in 2004, finishing runner-up behind Muller in 2003. The period represented the peak of Vauxhall's dominance in the championship.
Thompson moved to the WTCC with Alfa Romeo in 2005, winning on debut but finishing only eighth in the standings overall. He switched to SEAT Sport for 2006, balancing WTCC commitments with occasional BTCC appearances. Despite limited availability, he outscored SEAT's official BTCC number one Jason Plato on a points-per-entry basis. In 2007, racing an ageing Alfa Romeo 156 run by N.Technology — significantly less competitive than the works machinery — Thompson fought for the championship until the final round, ultimately finishing third in the standings.
He raced for N.Technology in a Honda Accord during 2008 before joining Lada Sport in 2009, making five WTCC appearances with a best finish of sixth at Imola. He returned to Lada for stints in 2012 and 2013, though the programme was hampered by mechanical problems and mid-weekend withdrawals.
Thompson won the European Touring Car Cup in 2009 at the Circuito Vasco Sameiro in Portugal, driving a Honda Accord for Hartmann Honda Racing. He successfully defended the ETCC title in 2010. He also competed in the Scandinavian Touring Car Championship in 2011 with Polestar Racing in a Volvo C30, departing mid-season over development disagreements. He made brief BTCC returns in 2009 and 2011 before stepping back from major programmes.
Thompson's career bridged the Super Touring era of the late 1990s and the modern NGTC period, winning back-to-back BTCC titles mid-decade. His ability to extract results from uncompetitive machinery — most evident in his 2007 WTCC campaign in the underfunded Alfa Romeo — was widely recognised by rivals and commentators.