Whitehead came from a wealthy Yorkshire family with connections to the wool industry. He began racing at the age of 19 in a Riley, progressing to an ERA B-Type with which he scored the first significant result for the Alta marque, finishing third in the Limerick Grand Prix. In 1936 he shared his ERA with Peter Walker and finished third in the Donington Grand Prix.
In 1938, while touring Australia on business, Whitehead took his ERA to Bathurst and won the Australian Grand Prix — his first major victory. He also won the inaugural Australian Hillclimb Championship during that trip. Back in England in 1939, he finished third in the Nuffield Trophy.
During World War II, Whitehead served as a pilot with the Royal Air Force. He returned to racing immediately once the sport resumed, finishing second in the British Empire Trophy at the Douglas Circuit on the Isle of Man in 1947, and racing in the Lausanne Grand Prix.
In 1948 he survived a plane crash at Croydon Aerodrome while travelling to Milan to arrange the purchase of a Ferrari 125. The accident left him seriously injured and absent from racing for a year.
Whitehead and his co-driver Dudley Folland were the first people to whom Enzo Ferrari ever sold a Formula One car — a Ferrari 125, in 1949, painted green with a red Welsh Dragon on the bonnet as a nod to Folland's Welsh roots. With it, Whitehead won the Velká cena Československa, becoming the first Englishman to win a major international motor race outside the United Kingdom since Richard Seaman.
He made his World Championship debut at Monaco in 1950 but did not start. At the Grand Prix de l'A.C.F. that year he came close to victory before a gearbox problem dropped him to third — his only World Championship podium in 11 starts between 1950 and 1954. He won two minor Formula One events during 1950, the Jersey Road Race and the Ulster Trophy, and continued to win in Formula Two across Europe in subsequent seasons.
Whitehead later drove Ferraris to victory in the 1954 Lady Wigram Trophy in New Zealand, which he repeated in 1956 and 1957. He also won the 1956 Rand Grand Prix.
Whitehead first started the 24 Hours of Le Mans in 1950, paired with John Marshall in a Jaguar XK120 and finishing 15th. In 1951 he teamed with Peter Walker in a Jaguar C-Type to win the race outright at an average speed of 93.112 mph (149.849 km/h).
From 1953 Whitehead concentrated increasingly on sports cars. At the 12 Heures Internationales de Reims in July 1953, he shared a Jaguar C-Type with Stirling Moss to win. He returned in 1954 in a full works-supported Jaguar D-Type paired with Ken Wharton to win again. He also won the Hyères 12 Hours during this period. Later in 1954, again with Wharton, he finished sixth in the RAC Tourist Trophy.
Whitehead's final major result came at Le Mans in 1958, where he and his half-brother Graham Whitehead finished second in an Aston Martin DB3S.
On 21 September 1958, the Whitehead brothers were competing together in the Tour de France automobile race when their Jaguar 3.4-Litre crashed off a bridge into a ravine approximately 9.1 metres (30 feet) deep near Lasalle, close to Nîmes, after overturning twice with Graham at the wheel. Graham survived with serious injuries; Peter was killed instantly.
Whitehead occupied an unusual position in the postwar racing world — culturally well-rounded, financially independent, and technically knowledgeable, he competed across Formula One, sports cars, and long-distance road events at the highest levels. His Le Mans win of 1951 and his victories at Reims stand as the clearest markers of a career that might have accumulated even more had it not been ended at the age of 43.