Most of my pre War B stuff is with a club member trying to get a B20 on the road. The hubs B20 to B23 are identical The hubs B24 to B 29 are identical They are all the same length fork to fork as the frames are all the same size so a B22 wheel will fit The lightweight wheels have loose ball bearings with cups & cones The heavy weigh ones have tapered rollers.
Bantam wheels are fine for the pre page lightweight B & L series but are too light for the "new"1936 on range
From memory M series wheels can be made to fit but the rear forks are wider so you will need to do some "fitting". They also run wider WM3 rims so look fat on a medium weight B Being in the UK you should be able to find some C10 / C11 wheels easier and they will also fill the space
The caveat is what are you trying to do with the bike Wrong wheels are fine for some weekend green lane riding but will get you an earbashing at any show .