Not Cooper, but Kieft.
It was announced in 1952 but (although styled on the 1951/2 Formula III cars) it used the chassis from one of the 1950 production Formula III cars (known as either C50s or Mk 1s). It used a BSA 650cc engine. Like the C50, it would run double wishbones all round, with Metalastik bushes as the springing medium.
Other Formula III manufacturers were skirting around motorcycle-engined road & sports cars (H-prod to Americans and popular across Europe with the likes of DB). Cooper had already produced the Cooper-Triumph T4 prototype (which survives and occasionally still competes) and Iota had demonstrated the P2 roadcar (which survives, but I don't believe is running).
It's not clear how serious Cyril Kieft was, and the car seems not to have been registered for the road. It is believed to have been either scrapped or converted back to Formula III spec. Apart from the ridiculous mudguards, she's rather cute, and I wouldn't mind building a replica - if only we could turn up a C50 chassis.