In 1934 Woolf Barnato commissioned Walter Hassan to make a Brooklands single seater basedon his Speed Six 6.5 litre Bentley. the car was named the Barnato-Hassan. In 1935 the engine was replaced by an 8 litre Bentley one and in thisform the Barnato-Hassan took the Brooklands lap record which was later beaten by Cobb's Napier Railton. The Barnato-Hassan survived the war and was fitted with a two-seater sports car body then later converted back into single seater form.
After building the Barnato-Hassan, wally built a similar car around 4.5 litre Bentley parts for E W W Pacey which was named the Pacey-Hassan.
(the above is a summary of what Denis Jenkinson wrote in The Sports Car Pocket Book)
So, the Barnato-Hassan was never supercharged. Although Jenks does not specifically say so, I would expect that the Pacey-Hassan was based on a 'blower' Bentley.
Incidentally the charismatic 4.5 litre 'blower' Bentley never won a major race!