Well,
I wonder it it's the Granger Archaeopteryx ?
The clues don't rule out a tailless parasol, it's in the 1930's, one built, a tractor Bristol Cherub engine and being "prehistoric" the fabric could be expected to be "delicate"
Edit:
I just found a three-view drawing and the cockpit, control wheel and other sketches seem to fit well.
SFA Forum - Print Page (cancel the offer to print and the drawing will appear)