Griffin came to motorsport relatively late, beginning his car racing in 2008 in the VW Cup. Over two seasons he collected three podiums and two race wins. In 2009 he entered two rounds of the Porsche Carrera Cup Great Britain at Silverstone with Motorbase Performance, before returning for a full 2010 season with the same team in the Pro-Am 1 class, finishing 21st overall.
Griffin joined the British Touring Car Championship in 2011 with Motorbase, driving under the Airwaves Racing banner in a Ford Focus ST Mk.II. He raced in the BTCC for three years, accumulating top-ten finishes and one front-row grid start courtesy of the reverse grid. In 2012, racing under the Redstone Racing banner, he brought out the safety car at Croft after crashing his Focus into the tyre wall and causing an engine fire. He missed Snetterton to attend to business commitments during the 2012 Summer Olympics, then returned at Silverstone to complete the final two rounds of the season.
In February 2013, Motorbase confirmed Griffin would return under the Addison Lee Motorbase banner for the Jack Sears Trophy, driving a Super 2000 specification Ford Focus. He opened the season with two class victories at Brands Hatch, went on to claim eight class wins across the year, and finished second in the Jack Sears Trophy Championship.
Griffin moved to GT racing in 2014, joining the Oman Racing Team with an Aston Martin V12 Vantage GT3. In 2015 he produced his strongest British GT campaign, winning at Oulton Park and Snetterton and finishing fourth overall in the championship with 123.5 points. In 2016 he switched to Barwell Motorsport for a Lamborghini Huracán GT3 season, winning at Oulton Park and finishing fifth with 98.5 points. He remained with Barwell in 2017, finishing fifth again with 134 points.
Griffin competed in the FIA WEC in 2015 and 2016 with Aston Martin Racing in the LMGTE Am class, driving an Aston Martin Vantage GTE. The 2015 season brought 14 points and a 19th-place classification; 2016 brought 24 points and 11th.
He made his Le Mans debut in 2016 with Aston Martin Racing, co-driving with Gary Hirsch and Andrew Howard, completing 318 laps to finish 36th overall and seventh in class.
In 2018 Griffin returned to Le Mans with JMW Motorsport in a Ferrari 488 GTE alongside Cooper MacNeil and Jeff Segal, completing 332 laps for 30th overall and fifth in class.
Griffin's most successful season in endurance competition came in the 2018 European Le Mans Series with JMW Motorsport in the LMGTE class. He won at Paul Ricard and at Silverstone, added a second at the Algarve, and finished runner-up in the LMGTE class standings with 88 points.
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