The engine is a 196cc Villiers 2E engine. Made 1930-40. It is rarely possible to give the exact year of manufacture. You can only say that particular type of engine was made between this date and that date. It is the cheap cooking version of the 196cc engines Villiers made at that time but can be much improved by exchanging the standard cast iron piston with the aluminium piston fitted to the 196cc Super Sport Villiers of the same era. Super Sport pistons are also easier to find.
Given the frame number the VMCC or Fanny Bee owners Club can easily identify the year of manufacture.
Finally, Pathe News filmed a segment showing two workers from the Fanny Bee factory erecting one of those 'Built like a Bridge' frames. Its worth looking at.
All in all, a lightweight worth restoring.
Cheers,