Anyway, returning to the "AF" issue, I've just had a look at some of my father's spanners (probably 70-75 years old). Many have sizes cast or engraved on them described as "AF". For example, the left and middle ones in the photo below are marked "5/8 AF" and "9/16 AF" respectively, clearly far to small to fit a nut or head of a bolt with 5/8" or 9/16" threads of any type - and, indeed, have measured openings 'across flats' of approximately 5/8" and "9/16" respectively. On the other hand, the one on the right also has an opening of approximately 9/16" ('across flats'), but is marked "5/16 W", hence presumably designed to fit a nut or head of a bolt with a 5/16" Whitworth thread.
So, at least when it appeared as a marking on spanners, "AF" definitely meant "Across Flats", and had absolutely nothing to do with the thread of the fastener (whether Fine, Coarse, American, British or anything else)!