Hansford began racing motorcycles in Australia, winning the 1973 500cc Unlimited title, as well as competing in the New Zealand Marlboro Series in 1975/76 and 1977/78 on Team Kawasaki 750s. He also won one leg of the 77/78 series on a KR250. In 1978 he traveled to Europe to compete in Grand Prix motorcycle racing for the Kawasaki factory racing team. He finished 2nd in the world 250cc championship and third in the world 350cc championship in 1978. In 1979 he again finished 2nd in 250cc and 3rd in 350cc. In 1980 he teamed with Eddie Lawson to finish second in the Suzuka 8 Hours event, but suffered severe injuries in 1981 at the Belgian Grand Prix at Spa forcing his retirement from motorcycle racing.

With 10 Grand Prix victories to his credit, Hansford is ranked fourth for the most Grand Prix wins by an Australian behind Mick Doohan (54 wins), Casey Stoner (38) and Wayne Gardner (18).

Hansford then turned to touring car racing in 1982 with Allan Moffat Racing. He had previous ties to the Moffat team and was actually entered to partner Colin Bond in the second Moffat Ford Dealers Ford Falcon in the 1977 Hardie-Ferodo 1000. However, a motorcycle racing crash caused injuries which saw Hansford forced to withdraw from the race and be replaced by open wheel driver Alan Hamilton. The car he was to drive with Bond finished second in Ford's famous 1-2 victory at Bathurt in 1977.

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