I started off looking at those Rob and drifted into despair....
Engine number KM20 101 is also listed as being a Standard fitted to frame 2290 (Tally no.5952) and despatched 10/3/1939 to W. Briggs; Hulme...and as a DL installed in frame no.156 (Tally no.5977) and sent to Millard, Guernsey on 29/11/1938
We therefore seem to have the following Tally numbers for frames fitted with engine KM20 101 :-
Four identically numbered engines...three identically numbered frames...plus the M21 that I don't have records for...no wonder we're confused ! This is absolutely the norm for late 1930s BSA records...Their habit of using one frame prefix for four different versions (M20 / 21 in Std and DL) was hard enough and then they started trying to supply matching numbers for Government contracts and ended up re-stamping numbers that they had already applied to non-matching bikes !