Hawkins participated in three Formula One World Championship Grands Prix, debuting on 1 January 1965 at the South African Grand Prix in a pushrod Ford 1500cc-engined Brabham Formula Two car. Like fellow-Australian Frank Gardner he started with the John Willment Automobiles team. He scored no championship points, as his best finish was ninth on his debut. He did have two podium finishes in the non-championship Rand Grand Prix, held in South Africa. He finished second in 1964 and third in 1965. In 1964 he won the Rhodesian Grand Prix in the Brabham and in 1965 he also won the Cape South Easter Formula One Trophy. He was a non-starter in the 1965 British Grand Prix and retired from the German Grand Prix that year with an oil leak.