Xausa,
your "new" .375 H&H Magnum seems to be a very early one, at least the barreled action. The Mauser serial number and the German BU (only)proofmarks date the action to 1911. The service load for the 300 gr bullet, 56 gr Cordite, is very early too, as the 1925 Kynoch catalog does not list the .375 H&H loaded with Cordite any more. Instead, the 1925 load was 60 gr (unspecified) Smokeless.
Apparently the rifle was restocked later, as the style is not consistent with an "about WW1" date, as is the clarifying inscription 375 H&H MAGNUM in post-WW2 font.