Tom,
You really want someone like Hilary Stone to answer this, but the
threads certainly won't be metric or SAE. They will be cycle or just possibly
BSF. Cycle (CEI) is most likely though BSA often used their own threads on
motorcycles so probably also on bicycles. If it is a very small tapped hole,
it might be three sixteenths CEI. If so, 2BA should fit as that is 31.4 TPI
against the 32 of CEI. If there is a larger diameter portion locating in the
chainwheel, turn up a suitable spacer and tap it to the same thread. I've
done that on Williams cranks and it works fine.
Stuart Tallack in Sussex