Williamson won from 1998 to 2007 various titles in karting. In 2008, he debuted in Formula racing and participated in the winter series of the British and Portuguese Formula Renault. In 2009 he started for CRS racing in the British Formula Renault and finished tenth. 2010 Williamson moved to Manor. He finished the season in second place behind Tom Blomqvist and drove in 19 races five times the pole position out, also won five times and scored four fastest laps. On October 14th and 15th 2010 Williamson tested at Estoril a GP3 Atech CRS Grand Prix of Boldien and scored with 1:31,432 and 1:31,230 minutes on both days Nachmittagsbestzeit. At the end of the year he was recognized for his achievements with the McLaren Autosport BRDC Award.
2011 Williamson went for MW Arden in the GP3 Series at the start. After four races without points he scored with a second place finish his first podium finish of the race series. Three races later his first GP3 victory. He finished the season off on the eighth championship course and sat down within the team with 31 to 29 points from Mitch Evans by. He also participated in two race weekends of the Formula Renault 3.5 for ISR. He finished the championship without points at the 33rd rank. After the season, Williamson completed his first Formula 1 test for McLaren. 2012 Williamson went first for Arden Caterham in Formula Renault 3.5 at the start and was admitted to the funding of Red Bull. After he had remained on the first three race weekends with no points, put his Red Bull a promotion and he lost his cockpit. His successor, António Félix da Costa finished in fourth place overall and several victories. Williamson then returned to the GP3 Series. There he played the second half of the season for Status Grand Prix. With a fifth place as best result he was 17 in 2013 Williamson received a GP3 cockpit with Bamboo Engineering. Although he remained winless in contrast to his teammates Melville McKee, he won the most points for the team and finished the season in twelfth place in the drivers' standings. A third place was his best individual result.
- 2010: British Formula Renault (2nd place)
- 2011: GP3 Series ( 8th place)
- 2011: Formula Renault 3.5 (ranked 33)
- 2012: GP3 Series ( 17th)
- 2012: Formula Renault 3.5 (ranked 32)
- 2013: GP3 Series ( No. 12 )