Fazakerley didn't re-number rifles unless there was a specific reason, such as a lost or pbliterated number. Then it was numbered with a ZZ prefiz number, allocated by the War Office ort after 1955 or so with the new type that showed all and sundry that it was a re-number, such as SA68A 1234 and so on.

We know BSA renumbered SOME, but not by any means all, of their FTR rifles. But they could do what they liked, because they were an independent contractor. A good example is No4 Mk1/2 53P12345. Made at BSA as P-12345 it's FTR'd in 1935 at ROF6 Fazakerley and emerges as a Mk1/2 but still P-12345

Rifles that were FTR'd were never classified as new rifles. The criteria was that every part that went through the FTR system was gauged against a 'life'. All had to give give a further 80% life. Parts that cound not gauge to give a further 80% life were scrapped. No rifle left the FTR programme or even a Base Workshop with a No3 bolthead either