Friend, I would REALLY like to know just how you are doing that measurement.
This is a trick I often use myself, but I do it with a CANADIAN-made military Ball cartridge. Canadian .303 ammo nearly ALL had slugs of .312" diameter, unlike many foreign makes (especially American makes) which seem to favour the .311 slug. A .312 slug will always give better accuracy in a .303, ANY make or model, this by testing dating back to before the Great War.
What I do is put the Ball cartridge into the muzzle gently and see how far the cartridge casing stands out from the bore. A brand-new, absolute-minimum barrel will still have it stand out considerably less than a quarter of an inch. You set the cartridge in, let it find its position, then you push on it just a bit and give it a careful twist. This scribes a line around the circumference of the slug.
You measure this line and you have the bore diameter of that rifle at the muzzle.
As to if an 'iffy' barrel can be made to shoot, remove the bolt and check the bore visually. The rifling should he sharp and stand out plainly. Edges of the lands should not be rounded. The first inch or so of the bore is extremely important, but the British did find that a barrel with a worn leade still could be made to shoot acceptably with the .312" bullet just so long as the final 4 inches of the muzzle-end were good.
Believe it or not, they did a test on a brand-new barrel in 1908, using Ball ammo which was loaded with the highly-erosive Cordite Mark I powder. They started with a brand-new barrel and fired the rifle continuously for 12,000 rounds before they decided that it was worn-out. Shortly after that, they came out with Cordite MD-T powder.... which was/is FAR LESS erosive than the Cordite Mark I, which has not been made for rifle use since 1911. How long a barrel lasts with the post-1910 powder I have no idea, but it HAS to be a lot better than 12,000 rounds. A description of the test can be found in the TEXT BOOK OF SMALL ARMS - 1909 on Pages 137/8.
Check your barrel again, friend; it just could be a good one.