Buxton began competing in circuit racing in the mid-1990s, progressing from karting into production car series. In 1997, aged nineteen, he won the British XR2 Championship — the Ford Fiesta single-make series — in his first full season, becoming the youngest champion in the series' history. A title-deciding race at Oulton Park in wet conditions, where he started from pole and held off pressure from experienced rivals to win, was his defining early result.
He finished third in the National Championship in 1998, then moved into the Renault Clio Cup UK. In 2000 he was runner-up with Chris Hodgetts Motorsport, taking one race win. He won the championship in 2001 with TSM Developments, then contested the series for a third year in 2002 with Mardi Gras Motorsport, finishing third overall with four wins.
In 2003 Buxton joined the British Touring Car Championship mid-season, replacing Carl Breeze at Vic Lee Racing's Team Halfords entry. He drove a BTC-Touring class Peugeot 307 from round six at Croft onwards, finishing eighteenth overall in the standings. He made a brief return to the Clio Cup in 2009 with Amery Motorsport, taking two podium finishes in limited appearances at Rockingham.
Buxton joined McLaren Automotive in 2010, initially assisting with road car development before moving into the Head of the Professional Drive Team role. In October 2020 he became Head of Customer Racing for McLaren Motorsport, overseeing British GT and other customer programmes with models including the 570S GT4.
In 2011 he co-founded Scuderia Vittoria alongside former BTCC driver Tom Ferrier, entering both the Renault Clio Cup and the British GT Championship in the team's debut season. The operation achieved fourteen wins across both classes that year, including a debut British GT victory at Oulton Park on Easter Monday with a Ferrari 458 Italia driven by Charlie Bateman and Michael Lyons. In 2012, alongside Ferrier and Mark Hunt, Buxton co-founded the Michelin Clio Cup Series, an entry-level circuit racing category run on standard road tyres with a budget conversion kit costing approximately £3,000, designed to lower the barrier to entry for novice competitors.
From early 2022 Buxton served as team principal and managing director of BTC Racing in the BTCC, overseeing the team's three-car Honda Civic Type R programme and mentoring driver Josh Cook, who had won races under Buxton's guidance. In September 2023 he joined Speedworks Motorsport as Head of Motorsport, taking charge of the Toyota Gazoo Racing UK BTCC squad. For the 2024 season he recruited Rob Huff and Cook to the team. Under his leadership that year Speedworks secured multiple podiums, including a 1-2-3 finish at Snetterton led by Huff, and finished sixth in the teams' standings with 266 points.
Buxton's career traces a path from grassroots single-make racing to some of the most prominent team management positions in British motorsport. His work founding Scuderia Vittoria and the Michelin Clio Cup Series reflects a consistent focus on developing junior racing infrastructure in the United Kingdom, while his decade at McLaren and subsequent BTCC leadership roles positioned him as one of the more experienced team executives in British touring car racing.