It'll work.
Probably only once, though.
That action was used to make some .308 target guns, and was a bit stressed at that. IIRC they welded up the mag well to stiffen the action a bit.
The locking lugs are a ways back on the action, and there is mucho flex.
I would kindly suggest that a .338 Lapua in that one is a recipe for disaster.
Fuggetaboutit!
Or at least make video of the test firing.
Cutting and rewelding SMLE's? With all the good actions available, that seems a fools game to me.
If you gotta build on that action, look at some of the necked up 303 cases, maybe even a 338/308.
There have been some nicely done 45-70's on those too, but that would be a different barrel.
Gonna have to watch the pressures, too, no matter what you chamber it to.
Sorry guy. I would not want to be next to you on any firing line with a .338 Lap in one of those actions.
Cheers
Trevor Jones