Davidson's career started in karting in 1987, he won several championships in Britain and Italy. In 2001 he was runner-up to Takuma Sato in the British Formula Three Championship.
In 2001 Anthony tested for the British American Racing team, and became their test driver.
Debut & Minardi (2002)
In 2002 he was drafted in to replace Alex Yoong at Minardi for the Hungarian and Belgian Grands Prix. He was out qualified both times by his team mate Mark Webber and spun out of both events.
Davidson moved to BAR for 2003 (which became Honda Racing in 2006) as test driver. He was ablle to race for the team at the 2005 Malaysian GP, filling in for an unwell Takuma Sato. However both his and team mate Jenson Button's engine gave up just 3 laps into the race. He remained at BAR/Honda until the end of 2006 season when he moved to the Super Aguri team and partnered Takuma Sato.
Super Aguri (2007-2008)
Anthony's best F1 positions were a string of 11th places. Whist running third in the eventful 2007 Canadian Grand Prix he hit a groundhog and was forced to make an unscheduled pit stop, he finished the race in 11th. He remained at the Japanese team in 2008, however the team suffered financial problems and withdrew from the championship after only 4 rounds, leaving the young Brit without a drive in F1.
Outside of F1
Anthony commentated for BBC Radio 5 Live, and has stood in for Martin Brundle for ITV Sport, most notably at the 2006 Hungarian GP, the race on which team mate Jenson Button claimed his and Honda's maiden win in F1.
He has been confirmed as part of the Radio 5 Live commentating team for 2009 alongside David Croft.