Barber began racing in the Formula Renault Campus series in France in 1998, winning the championship with six victories from ten races. He graduated to French Formula 3 for 1999, driving for La Filière Elf and finishing fourth in the class B standings across fourteen races with six podiums. That year he was nominated as a finalist for the Autosport BRDC Award but lost out to Gary Paffett.
Returning to Britain in 2000, Barber joined Alan Docking Racing for the British Formula 3 championship. He contested eleven rounds, finishing fourteenth overall, with a best result of sixth in the final race at Silverstone.
In 2001 Barber switched to British Formula Ford with Haywood Racing, finishing eighth in the championship with two podiums across thirteen races. He also competed in the Formula Ford EuroCup that year, taking third in the standings with one win from five rounds, and entered the Formula Ford Festival.
The 2002 British Formula Ford season represented Barber's career high point. Racing for the Duckhams team, he won eight of eighteen races, including the first seven consecutive events of the season. He claimed six pole positions and seven fastest laps, ultimately taking the championship with 487 points — a dominant margin. He also entered the Formula Ford Festival that year.
In 2003 Barber moved to the United States to compete in Formula Ford 2000 with Cape Motorsports. He won three races from eleven starts, took seven pole positions, and finished second in the championship behind American racer Jonathan Bomarito. He also contested the Formula Renault UK 2.0 Winter Series with Comtec Racing, winning two of four rounds to finish second.
For 2004 Barber returned to the United Kingdom and joined Comtec Racing in Formula Renault UK for a full season. He won six races, took six poles, and finished second in the championship standings behind Mike Conway, who later won the FIA World Endurance Championship.
Barber remained with Comtec in 2005, entering both the Formula Renault 2.0 Eurocup and the French Formula Renault 2.0 Championship. In France he won one race at Nogaro Circuit and finished eighth in the standings. His Eurocup campaign produced one podium from eight rounds, with an eighteenth-place championship finish.
In 2006 Barber was elected a full member of the British Racing Drivers Club. Following a period away from competition, he returned to British Formula Ford in 2008 for an eleven-round season, starting from pole position once and securing three podiums including a pair of second-place finishes at the final round at Brands Hatch. He finished twelfth in the championship. He holds an FIA Bronze categorisation.