If you have no experience with Enfields (or other rifles) then don't even consider accurising issues at this stage.
You really need to obtain a standard No1 MkIII and/or a No4, and spend a lot of time shooting them and understanding how they work.
IMHO, trying to accurise a No1 is a complete waste of time unless you already an accomplished shot with the standard rifle. Most No1s can be made to shoot very well in their standard military configuration. If you are not familiar with the existing tuning methods for the standard rifle, then you'll end up simply butchering an innocent rifle by trying to introduce different bedding.
In the case of No4s, I'd estimate that about 90% of standard rifles can already easily outperform the capabilities of their owners....
In terms of competition regulation, rifles (at Bisley) are categorised as "issued" ("service rifle A" SRa) or modified ("service rifle B" or SRb). A modified rifle will exclude you from standard service competitions, whereas a well-shot standard rifle is eligible for all competitions.
BTW, of the hundreds of rifles I have tested, the absolute top five No1s and top five No4s were all standard rifles. Its very subjective as to whether its the extra bedding that makes a difference at all. By far the greatest influences are (1) barrel condition (2) ammunition (3) the shooter...