The Bergara 300 WM I recently bought isn't as  handy as the No5 in the thick stuff.

I tried some 180 grain RN .308 bullets in my 303 just for giggles, they shoot accurately without tumbling.

I may find some older data and try the .308 diameter 220 RN in the shorty 303 and see how they do, I think even if I got 1900 fps, that will still flatten deer and bear in the thick stuff up close.

My no 5 shoots like bird crap with PPU factory 174gr and home loads with 174gr heads. The rounds are feet apart at 100 yards and the odd tumbler. I’ve put a new bolt head in as the “ no go” was closing. As the bullet dia is the standard .311. Plus as far as I know it’s possibly one of the first “batch” serial B333. Is the barrel burnt out. I’m looking at using .312 heads next to see it that improves things. 

One way of getting a baseline is to lay your hands on some decent quality MkVII ball rounds, at least enough to fire some groups to show you how your rifle performs with the ammunition it was designed and built for.  I've had a couple of local Lee Enfield guys do that - contacting me to sell them 10 of the Greek HXP rounds I have remaining to fire for group.

Handloaders attempting to sort out Lee Enfields have a lot more exploration ahead of them than they do with something else like a Remchester .308 Winchester.  The scores of threads here and elsewhere in getting the action and barrel properly fitted in the furniture, the condition of the barrel, etc. are just one part of the equation.

The other part is that the Lee Enfield/Mk VII ball round is a package where each was engineered to operate with the other (generally speaking).  This is a 4 MOA package (again, generally speaking); if anything is off in the package, grouping is going to perform a lot worse.  It is far more complex than purchasing the 174gr. bullets from PPU, Sierra, Hornady, etc - for one thing, those bullets are quite different than the MkVII bullet: boattails rather than open based, and not the internal construction of the ball bullet.

If you're looking to do more than kill tin cans for recreational fun at the local borrow pit and are trying to get the best out of the rifle, there's a lot of exploring ahead.  Aside from taking a deep dive into how good the condition of the stocking is, trying reloads with different bullet designs, different weights and different powders is the easiest and quickest way to hope for quick success.

My guess is the throat is burned out from shooting cordite loaded Mk 7 ammo. Though, the same happens eventually when shooting Mk 7z NC Powder loads, it just takes longer, but usually accuracy falls off more “gracefully” with Mk 7z. 

On a good barrel and well fitting forend, load development for the .303 is not at all difficult. 

If you see elongated holes in the target, it’s likely a shot out barrel. If holes look perfectly round, check the forend fit. Easiest thing to do first loosen the trigger guard front screw a few turns (or better still, remove it) grasp the rifle at the wrist with right hand and pull the forend forwards and back with left hand, you should not be able to move it at all. If it moves, you will need to shim the draws.  

There are other things to check with fit of the forend, but this is a start.