Agree with you re the SMLE. Have had them in 303-22Falcon & improved, 303-270 & 303-243 of all things! Currently have several 303's in No1 & 4, plus No 1 MkI & P14. Plus a 375NEf 2.5". So am certainly aware of the action strengths & weaknesses, as well as the reloading side.
Folks get hyped up over chasing speed, which is fine if that's what floats your boat, just don't do it with an SMLE or Enfield! It will only end badly.
With the 303-25 in one of these actions, you get a 10rd, fast cycling bolt rifle that will suit 90% of the hunting in this county. By using projectiles in the 90-100gn weight range you will take everything from rabbit to even red deer. Stalking skills & shot placement are the critical aspects of this, more so than the calibre/cartridge!
So, again, I say pick a projectile in that weight, develope an accurate load & concentrate on learning the range a drop of this load whilst improving ones accuracy with said rifle.