The SMLE action is from the turn of the last century, 1900 or so. "Weak" is a bit strong. Back then standard pressures, like say the ..30/'06 were 45K CUP. The original .303 load was in black powder! As said, a modern gun, Mark IV on, well made, properly loaded is the equal of the .308/ 7.62X51mm NATO. (.308 Works at 55K CUP.) I would be no happier trying to use a Mark I with modern cartridges than an early sprinfield with the crackable actions.
In US writings, gun magazines, the comment is often that the rear locking lugs let the bolt flex more, simple physics/mechanical engineering, and this reduces case life 'cause you have to resize more... Not a huge deal, but less of a problem with front bolt lugs like say the .03 Springfield or Mausers or??? Political spite a bit? I suspect... Not a big deal to the Commonwealth thru more than 2 wars/police actions, etc. but then they don't, as a rule, reload.
And, as said, why go to the great expense of making a .308 SMLE when you can buy them?... should be a whole lot cheaper... And the more modern steels should be well chosen to handle the higher working pressures... but if you must, surplus barrels are probably available... Not real common with the military use of auto and semi autos today, so a bit of a chore. LUCK.