So, it's got a four-cylinder engine, smaller than two litres, and a Hewland gearbox (although I must say that is probably not what was originally fitted to this car).
I just discovered that gilescooperuk asked a question I didn't answer: The engine is not from a bike.
It's not a Lenham and not a Beach. And it's not French, but maybe that's a good place to start when solving this?