Hi again,
Never heard of an R250 Villiers engine-ever. At the moment to entertain myself I am trying to assemble a list of all known Villiers engine numbers. That includes going through all original Villiers factory literature, ploughing through the old weekly "Motorcycling" from the start of Villiers to the end, listing everything found in the various published Villiers histories plus going through the local State Police vehicle records. You get the message, I'm really, really trying to list all their motorcycle engines and the engine identifying numbers. (We all have our little obsessions.) An R250 is not mentioned in any way, shape or form. Not a hint, not a jot nor a tittle. Nor does your engine look like a Villiers engine although there is a definite family resemblance.
Nor do I think the gearbox is Albion. I see nothing about it that shouts Albion and I can't see Albion not numbering something they made. How could you buy spares for it without some sort of identification so they knew what model gearbox you had. Both you and the factory would be in the dark. The combination hand and footchange idea was tried by a couple of firms. Was it Ural or BMW that had it until not that long ago? Like you I don't really see the point but factories still did it. It had nothing to do with push starting. Some also persisted with the heel operated footbrake long past its use by date and most riders thought exactly the same as you about it. Its not a very sensitive way to operate the brake but its not that uncommon.
Finally, Villiers didn't use that type of finned exhaust pipe nut before the early fifties. They started to use a screw on exhaust nut on some models in the mid thirties but they weren't finned. Your engine may just have the original exhaust nuts replaced with later finned items or be exactly what the tank says - a Monet Goyon engine. Not Villiers at all. Personally, I think its straight Monet Goyon and you just have to identify which model.
Cheers,