gavin In the grand scheme of things BSA used the British Standard Cycle thread system. That thread should be BSCy also known as CEI (Cycle Engineers' Institute). Measure the OD of the thread, that will give you the basic size eg 9/16", 5/8", whatever it is. The die you need is (for example) 5/8" Cycle.
Above 3/8" the thread comes as either 26 or 20TPI, depending on application. Yours looks like 20 TPI. That is what you need to order.
67-4183, the part pictured, appears in the '54/57 catalogue, carried over from '49/53. 67 4122 is the locking nut for a sidecar lug stud.
Just examined my frame, one with a single seat, no rear footrests. The hole is 15/16" on each side and neither side has a thread, which was a bit of a surprise.
Swarfy.