Might first start with the proof marks to see if we can identify the cartridge. Failing that, a chamber cast which should tell us more definitively. A rifle of that vintage will have either British or European proof marks. Mike's comment is right on with "Mueller" an unclear reference. Could be European-made but proofed in the UK but the cartridge should give a clue on this.
If it's a Brit .350 then we should likely look for a bespoke (especially so because it's unusual for the Brits to make an o/u) double rifle in, say, 400/350 which might have the 310 gr bullet proof mark; or the 350 No. 2 which would have the 225 gr bullet proof mark. They might have different weights of powder stamped, too.
Regards, Tim
