I agree with Duncan and wonder if this is another example of two great nations divided by a common language.
It sometimes seems to me that, whereas in UK English nicknames are given by other people, in US English people give themselves what they term nicknames.
To put it another way is "Otto Puzzell" what you'd call a nickname?
Returning to our automotive muttons, what carburettors did the Redex Special have when that bonnet top shows no sign of being high enough to clear the Bristol engine's usual three downdraught Solex?
I've had a quick look at Maestro Nye's definitive Cooper history - he believes that Jack's car was a quickly refurbished MkII prototype, probably sold (knowing how Charlie Cooper did things) as a new car. Records are thin on the ground, the Cooper way.
The MkI had the high bonnet line incorporating the air scoop for the Solex carbs, but the MkII had a clever split radiator, which included ducting of air to the carbs, thus there is just the small bulge for clearance. This appears on photos of the prototype, and is identical to the appearance on the puzzle picture.
BTW I think this photo shows both Jack's car and the one in the background in the puzzle picture. The latter car is a MkI and shows the difference in the two bonnet lines, and the original MkI air scoop. The actual height of the bonnet remains the same.