Born in Montrouge, Hauts-de-Seine, France, to an English horse-breeder father and a French mother, Grover-Williams grew up bilingual. During World War I his parents sent him to Hertfordshire; afterward the family resettled in Monte Carlo, where he developed a passion for automobiles and motorcycles. He adopted the racing alias "W Williams" to keep his early motorcycle competitions secret from his family. His connection to the arts came through working as a chauffeur for Irish portrait painter William Orpen in Paris; through Orpen he met Yvonne Aupicq, whom he married in November 1929.
By 1926 Grover-Williams was competing in Bugattis across France. His breakthrough came in 1928 when he won the French Grand Prix, a victory he repeated in 1929. That same year, driving a Bugatti 35B painted in British racing green, he won the inaugural Monaco Grand Prix, defeating the heavily favoured Rudolf Caracciola in a Mercedes. He won the Belgian Grand Prix at Spa-Francorchamps in 1931 and claimed the Grand Prix de la Baule in three consecutive years from 1931 to 1933. He retired from racing in 1933.
Grover-Williams enlisted in the British Royal Army Service Corps in February 1940 and served as a driver in France before being evacuated from Dunkirk in June 1940. His fluency in both French and English made him a natural recruit for the Special Operations Executive, which trained him and promoted him to second lieutenant. On 29 May 1942, he parachuted into France near Le Mans alongside fellow agent Christopher Burney.
Operating under the code name "Sebastian," Grover-Williams established the Chestnut network in and around Paris — a sleeper cell tasked with stockpiling weapons for the French resistance. He recruited fellow racing drivers Robert Benoist and Jean-Pierre Wimille into the network. Women, including the agents' wives, served as couriers, and operations were centred on the Benoist family estate near Auffargis, some 40 kilometres southwest of Paris. Between February and March 1943, Grover-Williams organised six parachute drops of arms and supplies for the resistance, and coordinated an effective sabotage effort at the Citroën factory in Paris.
The network unravelled in late July 1943 when German direction-finding equipment pinpointed the location of the network's radio operator, Roland Dowlen, who was arrested on 31 July. On 2 August, German Sicherheitsdienst officers were led to the Benoist chateau at Auffargis, where Grover-Williams was found hiding in a stable and taken prisoner. Robert Benoist was captured days later but initially escaped; he was later recaptured and executed. Jean-Pierre Wimille survived the war.
Grover-Williams was taken to SD headquarters at 84 Avenue Foch in Paris for interrogation. In January 1944 he was transferred to Berlin and imprisoned at the Reich Security Office. In March 1944 he was moved to Sachsenhausen concentration camp. In March 1945, under a Nazi decree ordering "special treatment" for listed political prisoners, Grover-Williams was executed, alongside SOE network leader Francis Suttill. The Commonwealth War Graves Commission records his date of death as 18 March 1945.
Grover-Williams is commemorated on the Brookwood Memorial in Surrey and on the Valençay SOE Memorial's Roll of Honour in France. He was recommended for an Order of the British Empire posthumously but the honour was not formally awarded once his death was confirmed. He was awarded the French Croix de Guerre. A statue of Grover-Williams in his 1929 Monaco Grand Prix-winning Bugatti Type 35 stands at the Sainte-Dévote corner at the Circuit de Monaco. The 2009 video game The Saboteur features a protagonist inspired by his life.