Because even then a true sporting gentleman knew that the proper way to hunt is with a fine single shot rifle.

Actually, prior to 1910 or so, there weren't many cartridges for magazine rifles that were truly capable of tackling dangerous game.
The big rimmed nitro cartridges were largely an evolution of their black powder predecessors. That meant that one would have to choose either a double rifle or a single shot rifle to be able to make use of the exceptional power the new cordite cartridges offered.
Now, after the introduction of the 416 Rigby, 404 Jeffery, 425 W.R. etc, the popularity of big bore falling block single shots pretty much died.
The truth is, the British nitro single shot was then and is today a very rare rifle, the totals of most maker's production not exceeding a few hundred examples.