Hancock grew up in a family embedded in motorsport, with both his father and older brother active racing drivers. He began karting at an early age and moved into single-seaters in 2003, competing in the Classic Formula Ford 2000 winter series in a Van Diemen RF82.
Hancock's 2004 full season in Classic Formula Ford 2000 ended with a second-place championship finish — just a single point behind the champion — with four pole positions, one win, and ten podiums. His performances earned recognition in the specialist press, including a Motorsport News Driver of the Day award at Silverstone. Financial constraints prevented him from racing in 2005; instead he spent the year as No. 2 mechanic at the Formula Renault UK team Welch Motorsport to develop his technical knowledge. He returned to Classic FF2000 in 2006 and again finished as championship runner-up, claiming three wins, three pole positions, and a podium in every race.
Hancock stepped up to the Formula Renault BARC Championship in 2007 with Mark Burdett Motorsport, finishing third overall and being named best rookie. His two pole positions and one win all came at Silverstone. During the year, the British Racing Drivers' Club awarded him a Rising Star invitation, with BRDC president Damon Hill among those recognising his potential.
In 2008, racing with Apotex Scorpio Motorsport, Hancock dominated the championship. He accumulated five wins, three pole positions, six fastest laps, and nine podiums for 130 championship points, wrapping up the title with a round still to run, holding a 44-point lead over closest challenger Johannes Seidlitz. A partial 2009 campaign in the main Formula Renault UK series covered twelve rounds before budget difficulties ended the programme, with a best result of fourth at Donington Park.
Hancock joined the FIA Formula Two Championship partway through the 2009 season with the MotorSport Vision team, replacing the late Henry Surtees and competing in car number 44. He entered from the Oschersleben rounds and contested six races across the final three event weekends at Oschersleben, Imola, and Barcelona. He finished 25th in the championship without scoring points, his best individual result an 11th place at Imola.
Following his Formula Two stint, financial constraints redirected Hancock toward GT and sportscar racing. In 2010 he became a Lotus factory driver, contributing to the development and racing programme of the Lotus Evora, including a class win in the FIA GT4 European Cup. He competed across British GT, the Asian Le Mans Series, the Michelin Le Mans Cup, the Blancpain Endurance Series, and the 24H Series over subsequent seasons, driving Ferrari GT3 machinery and other GT3 cars for various teams including Ecurie Ecosse, Fortec Motorsports, FF Corse, and Kessel Racing.
Notable endurance results include a class victory in the 991 GT3 category at the 2020 Dubai 24 Hours with MRS GT-Racing, a class win at the 2020 Spa 6 Hours, and podiums at the Silverstone 24 Hours.
Hancock made his Le Mans debut in 2021, racing in the LMGTE Am class with TF Sport in the number 95 Aston Martin Vantage AMR alongside co-drivers Ross Gunn and John Hartshorne. The crew completed 332 laps to finish 35th overall and fifth in the LMGTE Am class. The same TF Sport lineup also contested the European Le Mans Series GTE class that season across all six rounds, with one pole position among their results.
Hancock has established a parallel career in historic motor racing, competing in pre-1978 Formula One machinery and classic sports cars at events including the Le Mans Classic, Goodwood Revival, FIA Masters Historic F1, and Peter Auto events. He won both races in the 2016 FIA Masters Historic F1 Pré '78 series aboard a Fittipaldi F5A and has claimed wins at the Silverstone Classic and Spa Six Hours Classic. He has raced more than 50 different historic vehicles.
Alongside driving, Hancock works as a driver coach specialising in historic racing and Pro-Am GT programmes, and operates a karting business under the Ollie Hancock Competition brand.