Dispersal rifles marking and cutoff

I have a clean, all matching, non-import no.1 Mk. III (not mark III*) dated 1940. Dark bore but sharp rifling, should shoot good. It has the normal "B" for BSA and no cutoff installed.
Question #1- why were they marked only with the B? I've heard it was because of wartime pressures, but I find that to be a bit preposterous- surely if they had time to stamp the other markings they would have found time to complete the BSA inc. marking. Was it to conceal who the maker really was? Was BSA not proud of the less-than- perfect finish? There has to be a real reason.
Question #2- since it is a Mk.III, it should have the magazine cutoff. Were they not installed (seems reasonable)? removed? Or installed but later removed? Or is it a Bubba modification?
I know some of you guys knows the answer! Not me!

From memory.... The BSA factory was so badly damaged from bombing that the production of the rifles had to be "dispersed" to smaller work shops around the factory. Since production wasn't "technically" done at BSA, the rifles weren't marked as such.

Does the 4 and the 0 in the 1940 seem to be a different font than the 19?

The 4 not so much, but the 0 is definately bigger and a little off-kilter.
Thanks for the explanation, makes perfect sense to me!

I have seen at least one 1940 BSA which still had its magazine cut-off; it was a pre-Dispersal rifle.

I don't think the British themselves seemed to know if the SMLE should have a cut-off or not! They got rid of them in 1915, put them back sometime in the early 1920s, then seemed to have decided they were A Bit Silly and got rid of them but left the slot cut into the action just in case, and then decided maybe they would put them back in before Ze Germans bombed the factory and put an end to the question once and for all. :p

Colonel Enfield.... That sounds very much like something Colonel Klink would say...:D

The "Dispersal" of BSA factories was part of UK's war plan, and not a direct result of the bombing of the Birmingham factories - BSA had been relocating and dispersing its facilities since 1939. BSA in fact had 67 factories under control, and so the rifle production was only a minor part of this effort.

BSA made No1 MkIIIs to service specification (which included a cut-off and narrow piling swivel) until mid-1940. The last ones have an "L" prefix, and they also have the full BSA&Co logo on the butt socket.

From mid-1940, BSA switched to production of No1 MkIII* "Dispersal" rifles. These normally lack the cut-off, although production does include some MkIII action bodies as well. The early rifles are prefixed "L", but the majority of 1940-42 rifles have "M" and "N" prefixes. Its thought that the "B" for BSA was used because the rifles were built to war finish standards instead of BSA's extremely high commercial standard.