Brooke began racing in 1937 with a self-built special based on a Riley Imp chassis fitted with an 1,100 cc MG engine. He entered several events that season without major success but continued developing the car over the following two years. In 1939, running a Riley 1,750 cc straight-six engine, he achieved three podium finishes at Brooklands, a second place at Shelsley Walsh hillclimb, and a second place in the International Trophy at Silverstone.
World War II interrupted Brooke's career, during which he received the George Medal for his actions during the Coventry Blitz. He returned to racing afterwards, initially with his pre-war special before acquiring an ERA B-type. With the B-type he won the Grand Prix des Frontières in 1946 and claimed victories in hillclimb events.
In 1947 Brooke finished second in the Swedish Winter Grand Prix in February, though he retired from the Vallentuna F1 race and the Jersey F1 race the same month. He then purchased an ERA E-type, and with it achieved the first-ever race finish for that model — a fourth place — at the 1947 British Empire Trophy at the Douglas Circuit on the Isle of Man. At the 1947 French Grand Prix he qualified eighth but retired after a single lap with engine failure. He later sold the E-type back to ERA.
During 1948 Brooke resumed with the B-type, retiring from the Jersey F1 race but taking third in the British Empire Trophy and fourth in the inaugural Zandvoort Grand Prix. He then switched to a Maserati 4CLT entered by Scuderia Ambrosiana, finishing 11th in both the Grand Prix d'Albi and the 1948 Italian Grand Prix, while retiring from the Monza Grand Prix and the Penya Rhin Grand Prix.
In 1949 Brooke placed seventh in the Grand Prix d'Albi with the Maserati and retired from the Italian Grand Prix. He retired from the 1950 San Remo Grand Prix after eight laps, after which he scaled back circuit racing and turned to rallying, competing with a Triumph TR2. In 1955 he took part in the Monte Carlo Rally when the Standard Motor Company entered several of their Eight and Ten models.
In 1954 Brooke made an appearance at the Goodwood F1 race with a Connaught A-type-Lea Francis. Despite setting the fastest qualifying time, he failed to start the race.
Brooke was joint-principal of Coventry-based Speed Engines Limited, established in the mid-1950s with the ambition of building a British Formula One engine. The project was short-lived and only one example was produced.
Brooke's career spanned the era from pre-war British club racing through the formative years of post-war European Formula One, and he remains notable as the first driver to bring an ERA E-type to a race finish. His George Medal distinguishes him among the relatively small number of racing drivers who also distinguished themselves in wartime service.