It was pretty common for SMLEs to have their barrel bedding "packed" with greased cork, etc. An additional band was installed just behind the nosecap. There was pressure applied to the barrel, and the additional band helped keep the pressure applied, not relying solely on the rather thin handguard to do so. No. 4s were often center bedded, pressure pad at the forend tip being removed. The forend tip pressure could vary because of the length of wood between the action and the tip.
Service ball, both .303 and 7.62, tended to have velocity variations. Velocity variation tends to produce vertical stringing, most noticeable at long range. The group would be oval, the scoring rings are round. The vibration pattern of the Lee Enfields tended to launch slower bullets at the top of the vibration cycle, faster bullets at a lower point. This tended to make groups rounder. This only made a difference with service ball.
A lot of the .303 ball shot better than the IVI 7.62 ball, which did not have a good reputation. DA 7.62 was respected. In general, it was considered more difficult to get a service configuration 7.62 conversion to shoot as well as one in .303. After rifles no longer needed to be service pattern, there were all sorts of modified LEs. The OP's rifle is an example.
As far as SMLE grouping capability is concerned, I believe that in Australian James Sweet's book he mentions that a good SMLE, properly configured for competition, shooting decent .303 ball, could hold 3 moa. Doesn't sound impressive, but when the size of the scoring rings on the standard targets is considered, such a rifle would be competitive.