In fact - I'd hazard a guess that it is NOT the barrel failing.
The headspace 'wear' points on an Enfield are the locking lugs on the bolt/action.
The locking lugs are hardened (very thinly) and are virtually always the point of failure. It is important that the bolt locking lugs 'fit evenly' against the action lugs and the first few firings/recoil actually 'sets' the lugs - this is why you cannot just stick a 'new' (or second hand) bolt into an 'old' receiver. A new bolt needs FITTING in the proper sense of the term.
Notes from Peter laidler :
First things first. Bolts could only be fitted at Field and Base workshops because they were the only ones that had a 'GAUGE, Inspectors, Bolt'. This is a brand new, calibrated bolt. Still in white metal and marked as such. If my memory serves me right, the slot in the long/top locking lug is machined right through to identify it. So that's the reason if you have ever seen one. This bolt is bare. Clean the locking lug surfaces of the rifle and put a smear of 'engineers blue' marking dye onto the corresponding locking surfaces of the inspectors bolt. Insert this bolt RIGHT FORWARD, rotate it closed, then draw it backwards and forwards a couple of times to mark the mating locking surfaces of the rifle. Push it forwards, unlock and remove.
Examine the locking surfaces of the rifle. The blue witness marks should be evident. This ensures that whatever wear that has taken place on the rifle locking surfaces has taken place equally. If its not, then I'm afraid that the rifle is unserviceable.
BUT, that's not quite the end of the story because you won't have this 'Gauge, Inspectors, bolt' but it's only right that I tell you. Now for a little secret. If you have ever bought a rifle that has a sploge of red paint on the left side, adjacent to the internal left side locking lug, then you now know that the rifle was condemned for 'worn locking lugs'.
If you are going to fit a second hand or new bolt, then do the same thing. If the dye pattern is one sided, then stone the high surface of the bolt until BOTH locking lugs bear evenly against the locking surfaces of the corresponding surfaces in the body. BUT DO NOT ATTEMPT to stone the rifle to get a bolt to fit (you can only get to the right hand surface in any case ....). The rifle body is induction hardened at these points to a depth of .004 - .006" .........................................