No 1 MK III's did not have larger or smaller bolt heads, the No 4 Series did but not the No 3's. The bulge you have experienced is caused by the wear on the locking lugs or the "Crushing" of the barrel and bolt threads.
There are ways to repair this but none of them are cheap and will involve finding a new bolt body or taking the barrel off, adding a thread, putting the barrel back on and rechambering.
Depending on how big the bulge, it might be perfectly safe just a ##### to reload the cases fired in it. If it is too far gone, it is not worth the effort or the money to repair it. Got a photo of a fired case?
Scott
OK, I have a couple of No 1 mkIII bolt heads with headspace numbers on them and if you measure them, they are different lengths.
OP, I find it strange that the gunsmith told you the face of the bolt head was worn. IMHO, that's IMPOSSIBLE. Those bolt heads are HARD. Anyone that's tried to machine one can vouch for that.
What can happen is the threads can be deformed very slightly but even that would be highly suspect IMHO, because deformed threads make thing very tight when rotating the bolt head. It's a very noticeable condition.
What can happen, occasionally, is that the action will stretch a few thousandths of an inch. Without seeing pics I can't definitely say for sure, but I believe that what you're seeing on your fired cases is NORMAL for both No1 and No4 rifles. There might also be some set back in the bolt lug recesses or the bolt lugs may be worn. Again very rarely.
Their chambers are cut slightly oversize on purpose, to facilitate feeding and closing the bolt on slightly dirty or otherwise oversize cases.
I only have ONE Lee Enfield that doesn't give an expansion ring at the web and that's only because I set back the barrel one thread and recut the chamber with a borrowed match reamer. All have in spec headspace.
Likely your gunsmith isn't familiar with the nuances of Lee Enfield chambers and doesn't have proper headspace gauges for it.
If you're going to hand load for the rifle and want your cases to last, neck size only and maybe just partially resize the shoulder area, without setting back the shoulder. This will fireform the brass to your particular rifle's chamber. To fireform you brass safely, get some small rubber bands from Staples and push them up the case to the rim before chambering the round. This will hold the case against your bolt face. After the first firing and neck sizing, the brass will be custom formed for your rifle's chamber, with no headspace issues.