Holland & Holland indeed made rifles for a belted .375 cartridge on Mannlicher-Schoenauer actions before WW1, see the H&H catalog page 52:
http://www.rbsiii.com/nitro_express/H&H_1910_Catalog.pdf
But it was not the now familiar .375 H&H Magnum, but the much smaller .400/375 H&H Belted Nitro Express aka 375 Velopex, the first belted cartridge commerially offered. This cartridge was meant for stag and antelopes, not for dangerous game. It used rather light bullets at moderate velocities. Kynoch today offers it loaded with a 230gr bullet @ 2400 fps from a 27" test barrel.