It is indeed a Rochdale Type F body. My source was a well-known historic racing forum, and the information which helped me was all about racing specials built with Rochdale bodies. Hence my previous incorrect guesses.
Interestingly, this wasn't the only car of this type - Ken Flint also built a Cooper-MG based on a MkV chassis, powered by an MG linered-down to 1100cc and fitted with a Marshall blower. I've looked at a photo of a MkV chassis, and can't see quite how they did it, or why.