It was a fairly common conversion from .400/.350 Rigby to .375 H&H, but since the action was built with a slant magazine box to accommodate the rimmed Rigby cartridge, I see no reason why it could not have accommodated a rimmed .375 H&H as well. The action looks like the slant box version to me.

This is my .350 Rigby Magnum, built on a slant box action. Notice the shape of the trigger.