Warwick was active in Formula One at the same time as Nigel Mansell, who would also become a Jersey resident for a number of years. Although Warwick was initially thought to be the better of the two drivers, he was never to win a race. Mansell went on to win what at the time was a British record 31 grands prix.
Warwick began his Formula One career with the fledgling F1 team Toleman for the 1981 season. He managed to qualify for only one race, the season finale at Las Vegas. Warwick had a mainly dismal 1983 season in the Toleman car, but bounced back, scoring points in the final four rounds of the championship.
He joined Renault in 1984 aged 30 after Alain Prost left them at the end of 1983. Warwick, expecting to have a race-winning car, led the Brazilian Grand Prix, his first drive for them, only to retire because of a suspension failure. He finished in second place in both the Belgian and British Grands Prix in 1984 and placed seventh in the championship. In his Formula One career he scored 71 points and was on the podium after four races.
Warwick moved to Jersey in 1985 and now operates a motor dealership there.