You said, "Enfield #14 1917". I assume you mean 1917 as the Pattern 14 was made in .303.

If by "done well" you mean it is already customized, then you could have a little more omph without changing the barrel by rechambering and/or reboring. Many people with 1917s kept the barrels on the rifle and had them rechambered for one of the standard .300 magnums.

If you are willing to go to the trouble and expense to do all that has to be done, then something like the .375 H&H is a good choice. I suggest you also consider the .400H&H in that event.

However, if you simply want to rebarrel or rebore to a larger caliber, why not go with something on the original .30-06 case head so you don't need to alter the bolt-face, magazine, and action? The .35 Whelen is available as a factory round and it would be great for that rifle. The .338-06, .375 Whelen, and .400 Whelen are good wildcats and some boutique ammo makers will even load those for you.