ConnormaxMax, with little info, did pick it right - no surprises there
This is a 'kidney' JAP design used on the JAP 80 and C80 models.
The one in your image is a Model 80.
Because Villiers owned JAP by this time, sometimes these JAP
engines were referred to as Villiers engines.
Easy Test: If you can remove the cylinder head it will be a JAP.
Villiers 2-strokes at this time had one-piece cylinders.
So, expand your search to include JAP Model 80 engines.
This is a waiting game but they do show-up at auction.
Hope this helps.------------------------------
Jack