Tom:
What Sarg said.
Watch the twist rate though if chambering the low velocity .375s in a double or single-shot. Long bullets like the Hornady spire-point will lose stability past 50 yds and key-hole by 100yds when fired from most barrels rifled for the H&H cartridge, dunno about those intended for Winchester's Big Bore. Best to stick to the lighter (ie shorter and faster) bullets, and short RNs rather than long spitzers.

The .375 JDJ is a great chambering for a cheap Lee Enfield sporter conversion though! Its about as much grunt as you can get out of a 'Smelly', and will feed 5 rounds from the original staggered box magazine. Mine likes the stubby 250gr Sierra spitzer a lot!