Turvey started karting at the age of eight before progressing to the British Cadet Championship in 1999 where he placed 5th overall and was selected to be a member of the English National team that went on to win the Inter-nation Championship. He graduated the following year to the Junior Yamaha National Championship where he won the title. Turvey spent a season in the Junior KTM before moving to the Junior Rotax class in 2002 where he won once again.
He graduated to single seaters in 2003 where he debuted in the British Formula Renault Winter Series. Turvey went on to spend the remainder of his season competing in the Zip Formula where he finished as the highest placing rookie. For 2004, he raced for 18 races in the Formula BMW UK where he took a race win and 7th in the standings. Turvey also made hi Formula Three debut in the Asian F3 Championship for two races. He stuck with Team SWR for his second year in Formula BMW UK for 2005 where he took 6 podiums to place himself 8th in the standings. He also competed with the team in the BMW World Final where he finished 22nd. Turvey competed in both championships once again in 2006 but made the move to Team Loctite/ Team Loctite Yamaha. In the world final he finished 6th while in the UK Championship, he took runner up with 10 podiums of which half were wins with 7 pole positions.
2007 was a much busier year for Oliver as he competed in two races with Porche Motorsport in the Porches Carrera Cup Great Britain, three races in the Formula 3 Asia Pacific championship with JA Motorsports where he finished seventh and two full time championships. Fulltime, Turvey joined Jenzer Motorsports to race in the Formula Renault 2.0 Eurocup and the Formula Renault 2.0 Italy Championship. In the Eurocup, Oliver managed 51 points with a single podium to place 8th in the standings while in the Italalian Championship, he finished 9th with 176 points with two podium finishes. In 2008, Turvey made the move to Formula 3 when he entered the British F3 International Series in the International Class with Carlin Motorsport where he took 4 wins and 13 podiums to earn 234 points. Alongside that, he raced in the Windsor Arch F3 Macau Grand Prix with the team where he finished 7th.
Turvey made his debut in Formula One as a test driver for Vodafone McLaren Mercedes in 2009 alongside his season in Formula Renault 3.5 Series with Carlin Motorsport. During Formula Renault, he claimed 5 podiums and a single win to finish fourth in the standings. Between 2009 and 2010, Turvey made his GP2 debut when he joined iSport International in the GP2 Asia Series where he took a single win and 6th in the standings. He continued to be a test and reserve driver for McLaren into 2010 while also moving to the GP2 Series full time with iSport. Just like in the Asia Series, he finished 6th in the standings however, he managed 4 podiums. 2011 was a repeat of 2010, Turvey continuing to test and reserve drive for McLaren, however he only competed in two races of GP2 with Carlin and 4 races of the Asia Series with Ocean Racing Technology. Oliver continued to test and reserve driver for Vodafone McLaren Mercedes in 2012 and 2013.
Heading into 2013, Turvey joined MRS GT Racing in the FIA FT Pro Series where he raced for two races. He also made his debut in Endurance Racing by joining Jota Sport to race in the LMP2 Class of the Le Mans 24h where he finished 7th. Oliver also raced with the team in the FIA World Endurance Championship and the LMP2 European Le Mans Series where he finished 3rd. He continued to stay in Endurance racing in 2014 where he stuck with Jota Sport to race in the LMP2 Class of Le Mans 24h where he finished first to take the championship. He competed in the LMP2 FIA World Endurance Championship where he finished second in 2015 before making his debut in Super GT Japan with Drago Modulo Honda Racing. In his rookie year, he came 12th. Turvey stuck with the team and championship for 2016 for 5 races to finish 19th.
In 2018, Turvey made his return to the 24 hours of Le Mans with CEFC TRSM Racing but didn’t finish the race. He also raced with the team in the FIA World Endurance Championship between 2018 and 2019 where he raced in rounds one and two.
Oliver collected a variety of awards in his time including; The McLaren Autosport BRDC Award 2006, Sports Personality of the Year Award at the 2008 Cumbria Sports Awards, Daily Mirror Best British Driver in F3 Award 2008, The Dunhill Future Champion Award at the Goodwood Festival of Speed 2008, University of Cambridge Extraordinary Full Blue for Motorsport 2008 and the British Racing Drivers’ Club National Racing Driver of the Year 2008.
Turvey debuted in FIA Formula E in the 2014-15 season where he joined NEXTEV TCR for two races where he collected two points and 22nd in the standings. From there, he remained with the team for ten races in 2015-16 to take 11 points and 14th in the standings. He stuck with the team for a third year when they changed to NextEV and managed 26 points but finished 12th in the standings. For the 2017-18 season, Turvey returned with the team when they made the name change to NIO Formula E Team and got his first podium. He finished tenth in the standings with 46 points. The following season wasn’t as strong as previous years as he remained with the team for a fifth year but could only finish with 7 points, putting him 20th in the standings.