Webb began his motor racing career at the age of nine years in karting, where he was active until 2005. He also drove in the 2005 T -Cars - series in which racers aged 14 to 17 sedans were on the road, and was second in the Autumn Cup. In 2006, he focused entirely on the T Cars and was third in the championship.
In 2007 he moved to Formula racing and made his first experiences in the Winter Championship British Formula Renault, which he finished in 15th. Then he went to the British Formula BMW at the start and finished ninth in the overall standings. 2008 Webb participated in two Formula Renault Winter Championships and was fourth in the British and the Portuguese Second Winter Championship. Then he raced in the British Formula Renault, in which he finished in eighth place overall. In addition, he played four races in the Formula Renault Northern European. 2009 Webb remained in the British Formula Renault and denied his second season in the championship. Webb showed consistent and good and not only finished a race. With two wins and eight additional podium finishes Webb was at the end of the season third behind his teammate James Calado and the champion Dean Smith. He also appeared to four races of the Formula Renault 2.0 Euro to cups.
2010 Webb moved to the British Formula 3 Championship, in which he, as in Formula Renault, for Fortec Motorsport was launched. After Webb had given a good debut in the new series and had finished the first two race weekends, four out of six races in second place, followed at the third race weekend of his first two victories in the British Formula 3 Championship. At the end of the season, he finished with three wins third overall. 2011 Webb came for Pons Racing in the Formula Renault 3.5. With a sixth place as the best result, he finished the season starting on the 21st place overall, while his teammate Nick Yelloly who only drove the last third of the season, with a second place finish was 14th. In addition, Webb took part in four races of the North American Indy Lights for Jensen Motorsport. He scored a podium placement with a third place. At the end of the season, he finished 18th overall.
2012 Webb moved completely to North America and went for Sam Schmidt Motorsports, the reigning champions of last year, in the Indy Lights at the start. He started again from the pole position and third place was his best result. While Tristan Vautier, one of his three teammates, won the championship title, Webb was seventh overall as the worst Schmidt- pilot. For the 2013 season Webb returned to Europe in the Formula Renault 3.5. He received a cockpit with Fortec Motorsport. With a fourth place as best result Webb was 15th in the driver standings. With 27 to 214 points, he was subject to internal Stoffel Vandoorne.
- 2000-2005: Karting
- 2005: Cars, Fall Championship ( 2nd place)
- 2006: Cars ( 3rd place)
- 2007: British Formula BMW ( 9th place)
- 2007: British Formula Renault Winter Series (No. 15)
- 2008: British Formula Renault (8th place )
- 2008: North European Formula Renault ( 25th place )
- 2008: British Formula Renault Winter Series (4th place )
- 2008: Portuguese Formula Renault Winter Series (2nd place)
- 2009: British Formula Renault ( 3rd place)
- 2009: Formula Renault 2.0 Eurocup
- 2010: British Formula 3 ( 3rd place)
- 2011: Formula Renault 3.5 (ranked 21)
- 2011: Indy Lights ( 18th place)
- 2012: Indy Lights ( 7th place)
- 2013: Formula Renault 3.5 ( 15th place)