A quick glance at the despatch book shows that BSA started the 1939 season by continuing with the 1938 design of M22 engine, and up to 5/39 had produced about 350 of these engines with numbers prefixed KJM22.
Following on from that about 60 M22 engines with the redesigned crankcases; outrigger plate for the cams etc, were produced with engine number prefix KM22. The highest number I could see being KM22 192.
Some of the B series models also continued into 1939 with the earlier type crankcases, probably just a case of BSA using up what was already on the shelf first.
Engine KM22 108 and the frame it was fitted in is shown in the despatch book. Probably best I don't give more details as I don't own it or have been asked to by it's owner.
Fair to say that almost all of the bikes fitted with KM22 engines were exported.
Easy to swap the timing cover for a later example...