There is another catch, (or two)
The rifles were built around the ammo. All those odd little collars and spring plungers, and nose-cap muzzle-holes with an odd "window, ate there to optimize performance with a specific loading in a specific cartridge case.
Just as the boffins had to fool around a bit with the bedding regime at the changeover from Mk6 to Mk 7 ammo, every time you play with your reloads that use utterly different propellants, primers and bullets from Mk7 ball, you will be chasing your tail to squeeze consistent grouping and MPI at all ranges out to 900yds AND doing so with some vague reference to the numbers on the rear-sight leaf.
Number 4s using the EXACT same Mk7 ammo have a completely different bedding regime; and then there is the L42A1.
Making a new, "modern" barrel (.303" / .312") is the easy bit. Do you stick to the chunky "Enfield" 5-groove rifling to go with 5R / six-groove, or try one of the very interesting semi-ratchet, three-groove designs?
Original barrels can easily run out to .321" nominal groove diameter and still be within "spec" AND shoot up a storm. WITH MK7. The open-based bullet WILL "bump up" at the back end to seal in a good, concentric barrel with that sort of groove diameter.
Shoving closed-base, boat-tailed Sierras or Bergers through the same barrel may give disappointing results AND result in accelerated throat wear, especially if you shoot a lot and do a lot of rapid practices. Pre-loved "issue" .303 barrels that have digested a steady and protracted diet of Mk7 WILL have throats that are "flame-cut" to greater length and diameter dimensions than "factory new".
Original barrels have left-hand twist and the sights have "compensation" for the resultant "spin-drift" built into them. The front-sight base AND the "ears" of a SMLE nose-cap are offset fifteen thou' for this reason. Interestingly, the Canadians didn't seem to get too worried when they fitted 6-groove RH twist barrels to a bunch of No4s in WW2.
Plan "B" is to build a .30-.303, a chambering /barrel combo that has been around for several decades. .300 / .308 1:10" twist, just like a .30-06 barrel, BUT with a .303 chamber, cut using a reamer with a .299" pilot for the smaller bore. This actually works with the more abundant (and cheaper) .308" bullets out there. With a little creative carpentry, you can stuff a very chubby barrel under the woodwork of a No4 or even a No1. Naturally, the usual fun and games finding the "magic" load will ensue. Unless the reamer is custom-ground for a tight neck and throat (leade) this will NOT be a "bench-rest" chambering job, but it WILL function safely with .303 ball in a pinch. If you plan to ONLY EVER shoot .308" bullets no longer than the 168 SMK, you will probably get away with the even more common 1:12" twist barrel in your choice of Moly or stainless. If you are not doing virtually all this work yourself, carefully check the hourly rates at your local gun-plumber.