Hi Mike,
Can't help with the M/W carb I'm afraid. This is just to say that a single lever or double lever M/W are one and the same. You don't have to specify which one you want when you are seeking to find one. Whatever M/W you get you just build it up into whichever one you want.
As it happens Villiers continued with the double lever style right up to and including the 6E introduced in 1949. The throttle slide and jet cable assembly from the 4/5 cab as fitted to the 6E just drop straight in to your prewar M/W carb. Have a good look at the 6E spare parts list and you'll see what I mean. I bought my last set from Villiers Services.
Just be aware that Villiers manufacturing accuracy way way back when was nowhere as good as modern computerised parts so you may find the throttle slide either a rattling good fit or too tight to go in. I have a natty little holding fixture I use in my lathe so I can turn oversize slides to size if need be. It used to be that you could take your carb in to the dealer and sort through his stock to find the best fitting slide but unfortunately those days are long gone. It's make the best of what you find nowadays.
Finally, to finish off, the single lever style with natty little adjustment lever sticking out of the carb was just a cheaper version of the double lever. It saved the buyer a few pence at the expense of the rider losing the convenience of instant carburettor adjustment on the handlebar. The double lever style is much to be preferred and si the easiest both to source for parts and to ride with.
Cheers,
