Where are you? Every gun shop will carry .308" bullets. Not all will carry .311", but will order 'em. Mind you, .311" bullets may be too small for your rifle. Lee-Enfield barrels can vary in diameter from .311" to .315" and still be considered ok. Over .315" the barrel is shot out. The bullet makers make .311" and .312". None make 'em bigger, but go to .303british.com(add the W's). The guy there might still be making .313" and .314" bullets.
You need to slug the barrel. Hammer a cast .30 cal bullet or suitably sized lead fishing sinker through the barrel with a 1/4" brass rod and plastic mallet then measure with a micrometer.