Haslam was born in Langley Mill, near the Nottinghamshire and Derbyshire boundary, one of ten siblings. He began racing in 1972 on a 750cc Norton Commando, finishing seventh and eighth at Cadwell Park in wet conditions during his first outing. His early career was marked by personal tragedy: in July 1974 his elder brother Phil was killed in a racing accident at Oliver's Mount in Scarborough, causing Haslam to step back for the remainder of that season. In 1984 another brother, Terry, was killed racing a sidecar outfit at Assen in the Netherlands. Despite these losses, Haslam continued to compete at the highest level.
Haslam built his reputation on British short circuits, initially under sponsorship from Halifax car dealer Mal Carter and then with Honda Britain. In 1976 alone he recorded 16 wins. His versatility was exceptional — in 1978 he raced 125, 250, 500, 1000cc, Superbike, and Formula 1 machinery, and the following year became the first rider to win five different races in a single day at Oulton Park, a feat he repeated at Carnaby later that season.
Between 1979 and 1984 he won four British titles: the 1979 British TT Formula One, the 1981 MCN British Streetbike (winning seven of eight rounds), the 1982 British TT Formula One, and the 1984 ITV World of Sport Superbike series. His two World titles came in the TT Formula One crown in 1979 and the TT Formula Three championship in 1980.
At the Macau Grand Prix on the Guia street circuit, Haslam raced six times and won a record-equalling six times. His first victory there in 1981 was also the first time a four-stroke machine had ever won the event.
Haslam made his Grand Prix debut at the 1977 500cc British Grand Prix at Silverstone on a Suzuki, crashing out. He returned to Grands Prix in 1982 on Honda's experimental four-stroke NR500, scoring finishes at the Dutch TT, Belgian Grand Prix, and the British round. At the end of that season he took Honda's new two-stroke NS500 to Malaysia and won the non-championship Kuala Lumpur Grand Prix.
In 1983 Haslam joined a full factory Honda program as teammate to Freddie Spencer. He spent three seasons with Honda, including three years helping develop the unconventional Elf Honda prototype with its single-sided suspension front and rear. In eight years in the premier 500cc class, he recorded 61 top-ten finishes and nine podiums. His best single result came at the 1985 Dutch TT at Assen, where he finished second behind Randy Mamola — nearly 23 seconds clear of third-placed Wayne Gardner.
He also raced for Cagiva in the late 1980s alongside Randy Mamola and Alex Barros, and in 1987 finished fourth in the overall championship behind Wayne Gardner, Randy Mamola, and Eddie Lawson. In 1993 he made a wild-card appearance at the British Grand Prix, finishing fourteenth and scoring two points at the age of 37.
Haslam also set a world speed record in 1986 on the Elf 500, claiming the Flying Kilometre, Standing Start Mile, and Standing Start 10 Kilometre records on a private banked circuit in France.
Haslam was one of the most prominent figures in the Transatlantic Match Races between Britain and the United States. In 1983 he was the overall top points-scorer across the three-day meeting, recording victories at Snetterton in the rain and at Brands Hatch. Britain won that year's series 245 points to 198, with Haslam contributing 70 of his team's total.
After his Grands Prix career, Haslam raced with Norton in British Superbike competition, finishing second in the 1991 championship. He contested various national series through the mid-1990s and into 2000, when he and Leon made history by becoming the first British father and son to race in the same Grand Prix — Ron in the 500cc class at Le Mans on a Sabre Racing bike, Leon in the 125cc factory Italjet event.
Haslam was voted MCN Man of the Year in 1981. After retiring from competition he established a race school at Donington Park, where he trained over 86,000 riders over 24 years and helped launch the careers of James Haydon and Karl Harris. The school closed in October 2020 due to difficulties arising from the COVID-19 pandemic. In July 2023, Haslam received an honorary degree from the University of Derby in recognition of his racing career and training work.