Lots of older shops on-line do old bike bits. There are literally millions of NOS spares lying about. Remember, in the 30s, 40s and 50s few people had cars and half the world rode British cycles. You can get an idea of which chainsets etc were used and either wait until you find similar ones or fit what you like the look of. It's easier not to bother with trying to fit modern parts and you really don't need more than 5 or 10 gears. I upgraded my 1958 Rudge Pathfinder from cottered to cotterless cranks and got a really nice NOS alloy chainset that looks just fine. ( If I still had the original bike I am sure I would have upgraded it). I also have a 1961 Pathfinder with original cyclo 8 speed fitted and the frame unrestored. Both are lovely to ride and neither, IMHO, in any way infringe the designers intent. In any case, if you keep the frame as it is you can gradually restore it as it would have looked the day it came out of the factory, while enjoying riding it on compatible parts in the meantime. I seem to have wandered off a bit, but I am sure you get the idea.
Unhelpful bike shop? Take your time, ask advice from those that know and NEVER use that LBS again. Simples!
Where are you? folk on here probably know a useful bits shop near you.
BB number. There you have me. Anybody else know? Left rear dropout was common, but some were numbered on the top of the seat tube or under the BB. Older and wiser heads may be of help here. At least it gives you two numbers to keep safe so you can always identify it.