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When we say "Corrosive Ammunition," it is generally the primer compound that causes the trouble. A lot of the earlier primers contained substances that attracted water from the moisture in the air, and thus tended to rust a barrel even starting overnight if they were not cleaned. These substances have a similarity to SALT, and need to be flushed out of a barrel before cleaning.
The standard way to clean a Lee-Enfield was to pour two pints of boiling water down the barrel from the breech end, followed by regular cleaning and finishing with a lightly oiled barrel.
The boiling water does three things: it flushes the "salt residue" from the barrel and it heats up the barrel, allowing the microscopic pores in the steel to expand, thus loosens up any residue in them, and third, it helps dry any droplets of water still left inside the barrel because of the heated barrel.. A special funnel, flat on one side, was actually issued for this, but you can easily make one with a STEEL funnel, flatten one side of the lip of it so it sets flush with the rifle, and a short piece of 3/8 inch copper tubing soldered to the spout that you can insert into the chamber.
While Military ammunition is still available, much of it is steel jacket or copper plated ammunition, and as mentioned, corrosive. It is much better to buy modern commercial ammunition, or some of the modern Imported stuff.
Better still, start to reload your own ammunition. For the cost of a half-dozen boxes of the commercial stuff, you should be able to buy a "Starter" reloading kit made by Lee Precision, along with a hundred bullets, a can of powder and a hundred primers. You will use about a half can of powder for 100 target loads, but this will pay for itself within the first three months if you fire a couple of boxes each month. Also, you can "tailor" your loads to your rifle, and get even greater accuracy.
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