Born in Oatlands, Surrey, and educated at Clifton College, Abecassis began circuit racing in 1935 driving a modified Austin Seven that became known as The Einsitzer. After a year away from racing in 1937 he acquired an Alta and built a reputation in English national racing during 1938 and 1939. In 1939 he won the Imperial Trophy Formula Libre race at Crystal Palace in his Alta, defeating Prince Bira's E.R.A. known as Romulus in wet conditions — a result described at the time as the only occasion the 1,500 cc car was beaten by a smaller-capacity machine in the British Isles. He also held the Campbell Circuit lap record at Brooklands at 72.61 miles per hour and broke the Prescott Hill Climb record on 3 July 1938 with a time of 47.85 seconds in his supercharged 1½-litre Alta.
When World War II began Abecassis joined the Royal Air Force as a member of the Volunteer Reserves. He became an experienced pilot and was eventually selected for the secret Moon Squadrons, ferrying agents in and out of occupied Europe in specially modified Halifax and Stirling aircraft. For his service he was awarded the Distinguished Flying Cross and was mentioned in dispatches. He reached the rank of squadron leader and remained with the RAF Volunteer Reserves until his discharge in 1953.
Abecassis returned to racing after the war with pre-war machinery. He won a race at Gransden Lodge in a road-going 3.3-litre Bugatti on 15 June 1946, and in 1947 finished second in the Swedish Grand Prix, held on a frozen lake at Vallentuna, driving an E.R.A. In 1948 he was runner-up to Bob Gerard in the Jersey International Road Race.
He partnered with John Heath in Hersham and Walton Motors Ltd., a dealership and garage in Walton-on-Thames, and together they assisted in developing the Alta GP car for the new Formula One regulations. When that project stalled, the pair built their own cars under the HWM banner while retaining Alta engines. HWM competed in the Formula Two class initially, and when the World Championship adopted Formula Two regulations in 1952 HWM cars became eligible for Grand Prix events. At their peak, HWM employed Stirling Moss and Peter Collins, and the Belgian Johnny Claes scored the team's first victory at the Grand Prix des Frontières on the street circuit at Chimay, Belgium. An HWM also won the International Trophy race at Silverstone in 1952 with Lance Macklin driving. When Formula One reverted to 2.5-litre regulations in 1954 HWM attempted a competitive car using an enlarged Alta engine without success, and the team contested only two further Grand Prix events after 1953.
Abecassis himself entered his only two Formula One World Championship Grands Prix in 1951 and 1952, both at the Bremgarten circuit in Switzerland. He was more successful as a sports car racer: he won his class at the 24 Hours of Le Mans in 1950, sharing an Aston Martin DB2 with Lance Macklin, and finished second at the 12 Hours of Sebring in 1953 partnered by Reg Parnell. In 1953 he built a personal HWM sports car powered by a Jaguar straight-six engine and raced it in British national events until 1956. At the 1955 Mille Miglia he drove a red Austin Healey 100S to eleventh overall, posting competitive times in the Rome section close to those set by Stirling Moss in the Mercedes 300 SLR.
The death of John Heath in an accident at the 1956 Mille Miglia ended Abecassis's racing career and he turned his attention to the HWM business. He became the British importer for Facel Vega and maintained strong motor industry connections, aided by his marriage to Angela, daughter of Aston Martin chairman Sir David Brown. He died at Ibstone, near High Wycombe, Buckinghamshire, aged 78. In September 2010 his son David Abecassis published a biography titled A Passion for Speed. His grandson Jonathan Abecassis has continued the family's motorsport involvement by competing in vintage sports car racing.
Abecassis occupies a notable place in early British motorsport as both a gifted pre-war driver and a constructor willing to challenge the established European teams in the infancy of Formula One. HWM was among the first British teams to compete seriously at world championship level and provided valuable early racing experience to drivers who would later define the sport.