Personally I think the 7x64 and its sister 7x65r is probably the ideal do it all cartridge for just about anything. And has been around since 1918 ish.
With a light 123 to 140 grain bullet its fast and flat shooting for long range open ground shooting with a point blank range of well over 200m - ie so you are not having to worry about range.
And yet it has always a fast twist barrel and long lead so you can shoot long 173gn bullets pretty fast -2650 fps plus, so you still get flat shooting over longer ranges, but are good for any animal that walks this side of where you legally need to use something bigger.
And they don’t seem to kick like a 30-06.
7x57 does pretty much what a 7x64 does, certainly in the 140 to 150gn weights, but doesn’t quite have powder for the bigger bullet weights.
And the 7x64 will do pretty much what the 7mm Mag will do but with less recoil, powder and expense.
I don’t think it became popular in the UK because it was a German invention, but was never anglicised in the same way as the 275 Rigby.
However in the interwar era there were plenty of similar cartridges - eg the 280 Ross which were quite popular. But post the WW2 the 270 became popular as the standard deer stalking cartridge - and I think was standard issue in the Forestry Commission etc
Truth be told I doubt many deer would tell the difference between a 270 win and a 7x64. On the continent the 7x64 is more popular than the 270
