It wasn't required of the Proof House under any law AFAIK,,or was it?
London didn't mark any yr of proof date or code of date/proofing till the early 70's I don't think.
They both work under the same proof laws of the land so I would think it was not compulsory in the 40's to do so.

Maybe they just didn't feel the need to reinstate the extra marking right after the War. Then someone had a different idea in 1950 and it started all over again.
Or perhaps a new suit at the helm of the Birmingham House in 1950 and decided he rather liked the old look.

None of it really has to make any sense.

Just my couple of pence..