There is a way to get more reloads but it is a little involved and you need to shoot the new ammo first at a range. What you do is place a rubber O ring or something similar over the round so that when you close the bolt, the round is pushed firmly back against the bolt. When you shoot the brass stretch will all take place at the shoulder. Remove the empty case, mark it with the serial number of the rifle it was fired in and neck resize only. Yes, it now means those rounds only work in that rifle, but it is s small price to pay for likely doubling the number of reloads the case will take.
The guys in the Enfield section of Gunboards do this all the time.
LVSteve is exactly correct in mentioning that you can fireform .303 cases to the oversized chambers that were drilled into these rifles after initial Western Front experience indicated it might be a good idea. One can actually fireform new unfired brass by using about 7 to 8 grains of a fast burning poder like Green Dot or Blue Dot ahead of a Large Pistol primer. Insert a small tuft of Kleenex or Toilet Paper and then fill the case with a filler like cream-of-wheat or something. I used Quaker Oats, ground up fine using a Coffee Grinder into a sifty-powder and fill the case (leaving NO airspace -- this is important:
NO AIRSPACES!!!) up to the neck which then you insert into some wax to pack tight the whole mixture. Put your O-ring around the case base and tightly close the bolt -- point in a safe direction -- and fire away. Your case is fireformed. I do like 50 at a time when I have new brass. Clean the rifle well afterwards to get all the wax and stuff out of your barrel before firing live ammo. This fireformed brass can be loaded using a neck-sizer only and will last many reloadings.
I was lucky enough to win an EBay auction recently on a Parker Hale 5A sight for the Number 1 Mk III*. This sight came with a nifty sight aperture that is adjustable for aperture size. Having read that the mounting screws for the 5A are getting "hard to find" I actually had bought a set of those separately many moons ago knowing that someday I'd find a 5A at a price I could afford that probably would not have the mounting screws. That premonition proved to be so right.
The 5A is a Bisley-type target sight that was made after the First War and was developed to fit onto the No.1 Mk III and III* rifles by simply changing out the trigger-guard screw and the safety screw for longer ones. It fits right on and despite initial impressions, it seems to fit solidly. I would not want someone to whack it with a ballpeen hammer of course, but it's certainly not wobbley when mounted. I locktited (blue) the two screws so she would stay mounted under recoil.
The 5A is click adjustable for up-and-down and side-to-side. As I said, the aperture is really nifty with a finger-dial adjuster that gives you a choice between five different actual aperture sizes. You can have a large hole to look through, or by simply clicking over the dial my pen is pointing at...
...change over to a smaller or médium sized hole. Really nifty, and the adjustments are tight clicks not apt to move unless you move them deliberately.
Nifty. Glad I got this.
As I live in a rather impoverished part of the World and run a business that depends on the local economy, I'm generally impoverished myself (although the weather is nice, let's never forget that. Perpetual summer is worth more to me than many-bucks-an-hour in the Frozen North so I'm not really whining about it). Also, draconian gun-laws mean ammo isn't there to buy. I must reload, and try to do so economically.
My particular No. 1 Mk III* has a .314 bore, somewhat larger than the factory jacketed bullets available on the market which would be almost impossible for me to get in quantity here anyway. Casting was in order. I got myself a mould from Accurate Molds, a company that allowed me to specify exact bullet diameters-for-lead-hardness before making the mould. I elected a .315 diameter 220 grain bullet using wheelweight mix which seems to give me a .316 bullet using closer to No. 2 alloy.
Without trying to advertise a product, let me just say that I am incredibly happy with this mould and the service from the company itself. This is the best mould I own to cast with, and I will buy more moulds from this company. It works exactly the way it's supposed to and makes a quality bullet that I had cut to accept a .30 caliber gascheck.
I reamed out a Lyman .314 sizer die using a dowel and some emory cloth to give me a .3155 die. Maybe more like .316 near the top with a slight taper -- it was done by hand. This works out really well. Using 22.5 grains of 2400 I get about 1,850 fps out of my Number 1, and remember this is with a honking 220 grain bullet that -- when seated crimped into the crimp Groove -- just fits nicely into the magazine with no wiggle room. Out of a friend's No. 5, the bullet still has a velocity of 1750 fps. Firing Mark 7 ball out of the Number 5 we found he lost 450 fps off the 2440 fps velocity normally recorded as "spec", although the Mk. 7 loads we used were giving 2390 out of my No. 1. Still, that's a huge velocity loss for the jacketed bullet and greatly increased recoil. My loading barely lost 100 fps in his Number 5 compared to my Number 1, and recoil was gentle. In other words, my loading out of a Number 5 is more powerful than the factory ammo after the velocity loss. Interesting, although I only tested the one example and cannot claim that this would be a universal result.
This loading gives me about 95% of factory power in something I can produce here. It seems to work almost P.O.I. to the issue sights out at 100 yards although as you get farther out it's trajectory does dive a bit more than the 174 grain FMJ Military Bullet would have. However, with the Parker Hale sight I will make up my own trajectory table and be done with it. This loading comes close to the original 1890 "Mark 1 Ball" loading, as opposed to the modern Mark 7 ball loading used later on in the wars. And I can produce this loading in quantity as long as I have enough 2400 and Large Rifle primers to load with. It has a very nice impact on the Metal Silhouette targets on our gunrange -- after all -- it's a Mexican gunrange and Iron Chicken came out of Mexico and they do shoot it here still.
With this bullet, the round is at Max Overall length, but it still works through the clips. There's no room for error, however, so I don't just try to push the rounds straight down in because often one bullet tip will catch on the front of the mag and tie up the works. I use two fingers straddling the bullets so they go straight down in with no wiggle-room side-to-side. This works fine, for all 10 shots the mag holds, one clip after another.
On the topic of Lee-Enfield clips, this may have been covered but if it has not, there is a small trick to loading them. To prevent feeding jams, bullet number 2 and 4 must be ahead of bullets 1, 3, and 5 in the clip. Here is a photo of how your loaded clip should appear.
Enthusiasts will delight in the small scene in the movie "The Trench" where Daniel Craig -- before he was 007 -- stops to check a young private loading Lee Enfield clips in a front-line trench the evening of June 30 before going over the top at the Somme the next day. No explanation is given to the audience in the film as to what he is exactly checking, or why it's so important. But this placement of the rounds is what mattered.
The Parker-Hale sight is fully adjustable, and the plates that the sight calibrates against can be moved and reset to give a true up-and-down "zero" and side-to-side "zero" from which all further shooting can be calibrated against. Since my load is pretty much established, I will determine 200, 300 and 400 settings and record them for myself. Clicking up and down will always return to basic zero, as well as windage can always come back to "zero" at will. It's a neat sight.
I have left the original Military sight installed for now. I intend to shoot some groups as soon as I have time using the original No. 1 Mk III* sight and then record further groups using the aperture sight to see what differences I encounter in group size and accuracy. It's an interesting rifle and it has been fun doing the restoration and the continuing load-development so I can play with it as I please. It's unlikely that here in the High Desert of Central Mexico I'll ever get a chance to shoot at a deer with it, however.
lol) After years of giving my older brother grief about hunting "in close" with a scope, I had to concede that a scope's going to help me pick my shots through the thick stuff, especially in low light conditions. My parcel is a combo very dense conifer wetlands and some thick hardwood. 
