There is no short answer to your question. Excessive head space is often involved, so you have to know something about headspace. Headspace on a 303 is controlled by the rim on the cartridge, which is designed to hold the cartridge head against the bolt face. If things are well worn the cartridge may have a fair amount of room to slide back and forth in the chamber.
When the trigger is pulled, the strength of the firing pin hitting the primer will drive the cartridge full forward in the chamber.
Then the primer fires and ignites the powder.
The pressure created stretches the case sideways and contacting the chamber walls, holds the case full forward, until the pressure against the head of the case pushes it back tight against the bolt face.
The result is the case has been badly stretched at its most vital area, just ahead of the so lid base, resulting in a shiny, weakened area, that seldom comes apart on the first firing, but may easily come, at least partially, apart on one, or a very few more firings. The result is that the first firing of the case has pretty well ruined that case for reloading.
Thus, many, if not all, of your fired cases you have are virtually not suitable for reloading.
Your most satisfactory solution would be for you to buy a box of 303 ammunition. You then have to devise a system of firing them, in order that your own rifle doesn't also stretch the cases on first firing, making them also useless for further reloading.
The usual solution is to put as small, O ring over the cartridge and of a size that will fit tight against the rim and when that cartridge is put in the chamber the bolt will close hard on it.
When it is fired, the cartridge will not be allowed to move forward on the strike of the firing pin and the empty case will be a perfect fit to your rifle.
Also, the shoulder of this fired case will have moved ahead to tightly fit the shoulder of the chamber. From here on in, you reload it to allow the tight fitting shoulder to control headspace and your simple Lee reloader should work great, by just neck resizing and your cases should last as long as they would in any other calibre rifle.