From 1992 to 1997 Robert Huff operation karting, in 1998, he drove in the British Formula Ford 2000, he was a driver of the Formula Palmer Audi Winter Series. He finished the season off with the 2nd place in the British Formula Vauxhall Huff was champion. In 2001 he drove in the British Formula Renault. In 2002 he was third in the Renault Clio Cup UK, a year later, he took first place at the UK Seat Leon Cupra Cup with three victories. In 2004 he drove for Seat, the British Touring Car Championship with a Toledo. He achieved 2 wins and finished 7th overall.
Since 2005, Huff travels in the World Touring Car Championship, the first year he finished 21st place on the RML Chevrolet Lacetti. In 2006 he was the same car 16 and 2007 9 ( with one win). 2008 so far has been his most successful year with the 3rd place overall and 2 wins. In 2009, Chevrolet Lacetti moved from the Cruze. He finished with 3 wins 5th place. In 2010, he was with three wins this season again third in the overall standings. In the 2011 season he was sent to eight victories, with only 3 points behind 2nd behind Yvan Muller. In 2012 he was able to bring with 5 wins the Tilel in the World Touring Car Championship, before Alain Menu. For the 2013 season, he moved to Seat and was fourth in the overall standings. In November, he announced that he alongside his compatriot James Thompson for Lada goes to the start of 2014.