Webster began his motorsport career in karting in 2008, where he was active until 2009. In 2010 he moved to the Formula racing. He competed in the Formula Renault BARC and reached with four podium finishes and a second place as best result a fourth place overall. In addition, Webster won the Winter Championship BARC Formula Renault. In addition, he participated in various races of other series. 2011 Webster improved in the BARC Formula Renault with three wins on the second rank. With 286 to 295 points, he defeated Dino Zamparelli. Following the season, he took part in the winter series of the British Formula Renault and finished fourth. 2012 Webster denied his third season in the Formula Renault BARC. He won five races and reached again the second place. This season he lost to Scott Malvern with 335 to 368 points. He also competed in the Formula 3 Masters.
2013 Webster received a cockpit at Grand Prix status in the GP3 Series. While his teammates Adderly Fong and Alexander Sims outdated points, Webster remained without points and ended the season in 28th place overall.
- 2008-2009: Karting
- 2010: BARC Formula Renault (4th place )
- 2010: BARC Formula Renault Winter Series (Master)
- 2010: Autosport Young Guns (11th )
- 2010: Monoposto Championship, mono 2000 ( 15th place)
- 2011: BARC Formula Renault (2nd place)
- 2011: British Formula Renault Winter Series (4th place )
- 2012: BARC Formula Renault (2nd place)
- 2013: GP3 Series ( No. 28 )