RE: .303 British.
The Lee-Enfield is the most effective bolt-action combat rifle ever made! It leaves a lot to be desired, if one is talking about a FINE SPORTING ARM. However, the same characteristics that make it a great fighting weapon also make it a rugged, effective rifle for hunting in horrible conditions like Africa and Alaska.
Now, there are a lot more powerful cartridges than the .303 British too, but loaded with the correct bullets for the job, the .303 will kill any game animal on this planet.
I have seen straight military SMLE's AND sporterized ones also that would shoot 1" groups with a properly developed handload, some of which used .308" bullets.
I would not feel bad if I had nothing but a Lee-Enfield to hunt with.