Warwick began motorsport in British stock car racing under the Spedeworth organisation, winning the Superstox English Championship in 1971 at age 16 and the World Championship at Wimbledon Stadium in 1973. His younger brother Paul Warwick also raced, progressing to Formula 3000 before dying in a racing accident in 1991. Derek finished runner-up in the 1978 British Formula Three Championship before graduating to Formula One.
Warwick joined the new Toleman team for the 1981 season and managed to qualify for only one race that year, the season finale in Las Vegas. After two difficult seasons in the underperforming Toleman car, he improved considerably in 1983, scoring points in the final four rounds.
Warwick moved to Renault for 1984 after Alain Prost departed, inheriting a car he expected to be race-winning. He led the Brazilian Grand Prix on his debut for the team only to retire with a suspension failure following an early wheel-to-wheel duel with Niki Lauda. He finished second in both the Belgian and British Grands Prix and placed seventh in the championship. The season was nonetheless the beginning of the end for the Renault factory team; neither Warwick nor new teammate Patrick Tambay won a race.
A critical turning point came when Warwick chose to remain at Renault for 1985 and declined an offer to join Williams-Honda. That Williams seat went to Nigel Mansell, who won two races with the team. Renault withdrew from Formula One at the end of 1985. A further blow came when Ayrton Senna, using his contractual right as Lotus's number one driver, blocked Warwick from joining the team, believing Lotus could not adequately support two championship-calibre drivers.
With no seat available, Warwick joined the TWR Jaguar sportscar programme in 1986. When Elio de Angelis died in a testing accident, Brabham owner Bernie Ecclestone offered Warwick the vacant seat. Warwick raced in both the Formula One and World Sportscar Championships simultaneously that year, as no events clashed.
Warwick joined Arrows for 1987 alongside Eddie Cheever. The 1988 season was his best for the team: the powerful Megatron (rebadged BMW M12) engine allowed him to finish seven times in the top six, earning 17 points and eighth in the championship. His best race was fourth at Monza, just half a second behind Cheever. In 1989 he came agonisingly close to his first victory. At the Brazilian Grand Prix, two pit stops with stuck wheels cost him more than the 17 seconds he ultimately finished behind winner Nigel Mansell. At the Canadian Grand Prix in Montreal, he led in the wet before his Ford V8 engine failed on lap 40 while running second.
Warwick finally joined Lotus in 1990 — four years after Senna's veto had blocked the move — but the team's glory days had passed, and the Lamborghini V12 engine proved both underpowered and unreliable. He described it as "all noise and no go." A frightening crash at Monza, where his Lotus left the track at the Parabolica and rolled down the front straight, left him uninjured. He was able to run to the pits and take the spare car for the restart. He scored only three points that season.
Warwick returned to Formula One for 1993 with the Footwork team after a three-year break, completing a full season and scoring four points. He retired from Formula One with 71 championship points across 147 starts.
Warwick drove for Jaguar in the World Sportscar Championship in 1986 and 1991. In 1992 he joined Peugeot and won both the World Sportscar Championship title and the 24 Hours of Le Mans.
After retiring from Formula One, Warwick drove for the Alfa Romeo works team in the 1995 British Touring Car Championship, though the season was disappointing. He subsequently co-founded the Triple Eight Racing team with Roland Dane, taking over the Vauxhall BTCC entry for 1997. Racing one of the cars alongside John Cleland, he won a wet race at Knockhill in 1998 before retiring from driving at the end of the year.
Warwick served as a fourth steward at several Grands Prix in 2010 and 2011, a role given to former drivers who advise the stewards' panel. He was president of the British Racing Drivers' Club from 2011 to 2016, succeeding Damon Hill and later being succeeded by Paddy Hopkirk. He also raced in the inaugural Grand Prix Masters series for retired Formula One drivers in 2005 and 2006. In 2015 he underwent treatment for bowel cancer.