I've had another go at John Bolster's "Specials" and I'm confused because I think I remember the car I shall suggest looking rather different. However, here goes:
The Attenborough Special had a Frazer Nash chassis but without the usual multi-speed chain drive. It had an MG ENV preselector gearbox followed by a 'Nash bevel box and then duplicated chain drives to a solid axle. The engine was a sohc 1950cc unit from the experimental Aston Martin "Atom" and the body was a narrow two-seater from a 200-mile-race Talbot-Darracq.