I think the "Not English Make" was in effect in the UK from 1925 to 1955...superceeded by other markings.
As I understand, any foreign made gun coming into the UK had to be inspected/proofed by one of the official proof houses before it could be owned and/or make its way into the retail trade.
I had a '41 "Black Widow" Mauser that had all those stampings too. It was a $ 1200 purchase that I sold for $ 1250 about 9 years later.
It had some story with it...gun captured by the Brits, brought back to England, for clandestine use by UK operatives behind the German lines. Never believe a story with a gun...