In 2005 Webb was selected to be part of Dorna’s MotoGP Academy project—which included participation in the Spanish 125cc Championship—and was confirmed for 2006.
After entering the 2006 Catalan Grand Prix as a wild-card rider, he has competed full time in the 125cc World Championship for the following five years, starting out in 2007 where he failed to score points in all but one of the races. In 2008 the season started off really well for Webb, claiming a career best fifth position in the third race of the season, however he could not keep this up and fell away towards the end of the season. 2009 was hampered by too many retirements and thus did not improve on his performances from the previous year. In 2010 Webb has been at his most consistent regularly breaking into the top 10 of the championship close to the end of the season. Webb joined Mahindra for 2011 and ended the season in 19th overall. The highlight of the season was a pole position in the final 125cc race, the first pole for Mahindra.
He stayed with Mahindra for 2012 but the season in the Moto3 World Championship was a disaster due to an under powered motorcycle and failed to score any points. He started 2013 riding for Ambrogio Racing aboard a Suter Honda but was released by the team mid season due to unsatisfactory results. He then signed for PTR Honda to contest the remaining four rounds of the Supersport World Championship aboard a Honda CBR600RR.
For 2014, he signed to ride in the British National Superstock 1000 Championship aboard a Kawasaki ZX-10R for the Moto Breakers team. He left after a few rounds due to poor performances and later joined Collisions Recovery to ride their Kawasaki ZX-6R in the British Supersport Championship, he finished the season in 24th position overall. He remained in the British Supersport class for 2015 but switched teams and motorcycles as he signed for Appleyard / Macadam & Doodson to ride a Yamaha YZF-R6.