In principle you should only need to replace the barrel but it depends what else has been done to it.
Some had the magazine 'well' plated and welded, some had it with just a wooden plug, and others somewhere between the two.
Some had the rear sights fixed / pinned.
If the rear sight is free to move and the magazine well is clear to use then nothing else (should) need be done.
Barrels from : SMLE No.1 MKIII .303 Barrels*|*e-GunParts.com