Warwick began in British stock car racing under the Spedeworth organisation, winning the Superstox English Championship in 1971 at the age of sixteen and the World Championship at Wimbledon Stadium in 1973. He moved into single-seater racing thereafter, finishing runner-up in the 1978 British Formula Three Championship.
Warwick made his Formula One debut with Toleman in 1981, managing to qualify for only the season-ending Caesars Palace Grand Prix in the TG181. His 1981 and 1982 seasons were difficult, but he scored points consistently in the second half of 1983. He joined Renault for 1984 after Alain Prost's departure, led the Brazilian Grand Prix on debut before a suspension failure, and took second place finishes in Belgium and Great Britain to finish seventh in the championship — the high-water mark of his Formula One results.
A decision to remain at Renault for 1985 rather than accept a Williams-Honda seat proved costly; Renault withdrew from Formula One at the end of that year. A further setback followed when Ayrton Senna, using his contracted number-one status at Lotus, blocked Warwick from joining the team for 1986. Warwick consequently moved to sportscar racing with TWR Jaguar while also driving for Brabham in 1986 following the death of Elio de Angelis.
He drove for Arrows from 1987 to 1989, his best season being 1988 with 17 points and eighth place in the championship on the strength of Megatron turbo power. In 1989 mechanical failures denied him likely victories in both the Brazilian and Canadian Grands Prix. A year with Lotus in 1990 yielded only three points, the Lamborghini V12 engine proving both underpowered and unreliable. Warwick returned to Formula One in 1993 with Footwork, scoring four points before bringing his Grand Prix career to a close. BBC Sport would later describe him as "the best British racing driver never to win a Grand Prix."
Alongside his Formula One career, Warwick competed extensively in sportscars. He drove for Jaguar in the World Sportscar Championship in 1986 and 1991. In 1992, racing for Peugeot, he won both the World Sportscar Championship and the 24 Hours of Le Mans — the headline achievements of his racing career outside Formula One.
In 1988 Warwick appeared in the Celebrity Car at the inaugural Honda CR-X Challenge, and the following year entered a two-car team in the same series with drivers including Robin Brundle and Roland Dane.
Warwick entered the BTCC in 1995 with the Alfa Romeo works team. Despite the team having dominated the 1994 championship, the car was underdeveloped for 1995 and the season produced poor results. At the opening round at Donington Park, Warwick was involved in a crash that sent debris into a BBC television camera, prompting commentator Murray Walker's celebrated quip about the £6,000 repair bill.
After a year away from racing, Warwick co-founded Triple Eight Racing alongside Roland Dane and assumed responsibility for running the Vauxhall BTCC works entry in 1997. Originally planning to serve only as team principal, he elected to drive one of the cars alongside John Cleland. In 1998 he won a wet race at Knockhill, his sole BTCC victory, before retiring from driving at the end of that season while remaining involved with Triple Eight for three further years.
Warwick deputised for Martin Brundle as Murray Walker's co-commentator on ITV for the 1998 Canadian Grand Prix. In 2005 and 2006 he competed in the Grand Prix Masters formula for retired Formula One drivers. He served as the fourth steward — a panel role reserved for former racing drivers — at three Grands Prix in 2010 and 2011, advising on incidents from a driver's perspective. He was president of the British Racing Drivers Club from 2011 to 2016, succeeding Damon Hill and being succeeded in turn by Paddy Hopkirk. In 2015 Warwick received treatment for bowel cancer. He operates a Honda franchise in Jersey.
Warwick's Formula One career is defined by proximity to results that never fully materialised — a front-row qualifying record, consistent points finishes, and two near-certain victories denied by mechanical failure. His compensation came through sportscar success, particularly the 1992 Le Mans win and World Sportscar title with Peugeot. His administrative contributions to British motorsport through the BRDC presidency and stewardship roles extended a career that touched nearly every tier of the sport.