Theoretical BORE size of the .303 was .303, although the British did allow it to go as low as .301 at times. A .304 gauge passing all the way through was a "fail" with a new barrel.
The Ross Rifle Company held .300 - .301 as their standard on many of the 1905 rifles, although this opened up a little with the 1910.
GROOVE size was supposed to be .311, but some .310s did get through.
Enfield riflng is especially difficult to measure, what with there being a land opposite each groove. This is exactly the same as with the modern "5R' rifling, which is simply a right-handed copy of Enfield rifling: odd number of lands and grooves, grooves deep and wide, equal to the width of the lands. Ross rifling was much easier to measure, there being only 4 lands on most Rosses.
The British did extensive experimenting with bullets and barrels over a large number of years. One thing they determined was that Enfield rifling has a DEFINITE preference for FLATBASED bulets. Another thing they determined was that almost ANY Lee-Enfield rifle will shoot better with bullets made to the upper limit of tolerance, which was .312. This all was known more than a century ago, yet people still insist on making bullets in .3105 and .311. I find this incomprehensable, myself; it's almost as if they don't WANT the rifles to shoot accurately.
That said, there are many reasons why a rifle might not shoot accurately. The Damned Crack is a very important reason and it is equally so with the Number 4 as with the old Number 1. If a rifle shoots wildly, the fore-end should be removed and checked for The Damned Crack; it is to be found at the rear end of the fore-end of the rifle, just ahead of the butt socket, right where the trigger/sear interface is to be found. The wood dries in our climate (the rifles, most of them, were made in comparativly wetter climates.) and this is the thinnest point in the wood, it has a lot of stress on it, and so it cracks right here. It is a simple matter to degrease The Damned Crack, glue it with Acra-Glas and clamp it for 24 hours, following which any excess glue may be trimmed and the rifle reassembled. The Damned Crack is responsible for more lousy shooting than half of the bad barrels in existence. The name, by the way, came from the old-time Bisley shooters; it is not my concoction. Any time a rifle suddenly loses any semblance of accuracy, or the rifle suddenly starts shooting 2 groups on the same target, The Damned Crack is to be suspected.
That said, many barrels were ruined by careless cleaning ("cord wear"). Generally, a barrel so worn would have been replaced or, at the very least, the wear would have been marked with the appropriate Inspector's stampng.
In Commonweath Service, counterboring barrels was not a general practice, although a few such rifles do exist. In civilian life, however, with the dearth of decent barrels, it is bound to become more common. The job can be done in a lathe with a boring bar, although a 3/8 end mill also does it very nicely. It may be necessary to clean up the new internal muzzle with a needle file; if this is necessary, proceed VERY cautiously.
Another reason for a rifle shooting all over Creation can be muzzle damage. This can assume many forms, including impact damage and corrosion damage (rust pits). Damage RIGHT AT the muzzle often can be cleaned up by recrowning the rifle. Depending upon the depth and severity of the damage, it may even be possible simply to recrown the muzzle with a ceramic/diamond dust stone, a few drops of motor oil, an electric hand drill and a few minutes of careful work. Severe damage can require use of a lathe.
Hope this helps.
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