The BSA parts books identify them as 3/16" so I think that they were originally 3/16" Cycle (32 tpi) .
2BA is very close to that but slightly smaller in dia and has a slightly sharper thread form.
Once manufacturing tolerances come into play 2BA will fit fine with good female nuts but I have personally had good success with using 10-32 UNF which is slightly larger than 3/16" and has a 60degree thread form and 32tpi.
My primary now has all 10-32 UNF Fillester head screws and they fit very nicely without touching the female nuts - worth a try given they are relatively common screw size.