Some 303 British rifles shoot very well with .308 bullets without going to the trouble of rebarreling. A lot of the ammo that was loaded by the USA for the Brits and others dureing WW2 was loaded with .308 diameter bullets. I have several different headstamps with early 1940s dates and bullets measureing .308 diameter.
Of course if you have an oversize bore, then you may, or may not, have a problem. I suggest that you try out some .308 bullets in your rifle, you may be pleasantly surprised.
I have two rifles that I shoot fairly often in 303 Brit that will group under 2 inches at 100 yds with .308 bullets in 180 grain spire point. One has a .314 bore and the other has a .310 bore. Go figure.
On the other hand, I have some others that will only shoot into 4-6 inches at 100 yds with any bullets, wether they be .308 or up to .314 (I have a few hundred old CIL .314 bullets). bearhunter