Born and raised in London, Fullerton grew up with ambitions to race in Formula One. Those plans were shelved after his brother Alec died in a motorcycle racing accident at Mallory Park in 1964, and Fullerton chose to restrict his competitive career to kart racing. He began to make his mark as a teenager, winning the British Junior Karting Championship in 1966, 1967, and 1968.
At 16, Fullerton qualified for the British team to contest the 1969 Karting World Championship but was not selected. Eligible also to race on an Irish licence, he competed at the World Championships in 1969 and 1970 under that flag with limited success. When he switched to his British licence in 1971 he finished fourth in the World Championship, and two years later claimed the title outright with Birel, the first Briton to do so.
Following his 1973 world title, Fullerton continued to dominate British and European karting. He accumulated eight British Championship victories across a career spanning two decades, along with four European Championship titles — including the 1977 Karting European Championship won with Zipkart.
The defining chapter of his competitive career began in 1978 when he joined the Italian DAP factory team, where his teammate was a young Ayrton Senna. The pairing remained together through 1980, producing a series of intense head-to-head battles. Team manager Angelo Parilla reportedly regarded them as the two best kart drivers in the world at the time. The 1980 World Championship exemplified their rivalry: Fullerton won the first final, only for his engine to fail while he was leading the second, leaving him third overall and Senna second. That same year, at the prestigious Champions Cup at Jesolo near Venice, Fullerton overtook Senna on the very last lap to take victory — one of the most celebrated moments in competitive karting history.
Fullerton retired from racing in 1984, closing out a singular career dedicated entirely to karting.
Fullerton's impact on motorsport extended well beyond his own racing results. At a press conference at the 1993 Australian Grand Prix, when journalists asked Ayrton Senna which driver had given him the most satisfaction in competition, Senna named Fullerton without hesitation. The moment was featured in the 2010 documentary Senna, introducing Fullerton to a new generation of motorsport fans.
After retiring from the cockpit, Fullerton established himself as a driver manager and coach, working with a remarkable roster of future stars. Among those he coached were Allan McNish, who went on to win the 24 Hours of Le Mans twice; Dan Wheldon, who won the Indianapolis 500 twice; Paul di Resta, who reached Formula One with Force India; Anthony Davidson, a Formula One driver and later Le Mans class winner; Justin Wilson, who competed in IndyCar; and Jake Dennis, who won the 2010 junior World Championship and later the Formula E World Championship. Fullerton considered McNish and Davidson his finest students.
He continued to work in karting management into later life, coaching junior British champions including Jake Dennis (2010), Callan O'Keeffe (2011), and Jehan Daruvala (2013). Fullerton settled in Melton Mowbray, Leicestershire.
The Champions Cup victory at Jesolo in 1980 — passing Senna on the final lap — stands as the single most-cited moment in Fullerton's racing biography. Senna's own tribute at the 1993 Australian Grand Prix press conference cemented Fullerton's status as one of karting's greatest-ever competitors, a driver whose entire professional life unfolded in a single discipline without the detour to single-seaters that most of his peers attempted.