Relic Nut, the "more specific" identification of your find is, a civil war era tompion made in England for use in a British Enfield .577-caliber rifle. As the photos at the link posted by Duggap show, this type of tompion had a thin brass disc on the end of the long central shaft to hold the cork cylinder in place. That disc is broken off of the tompion you found, which is why it got discarded by the soldier.
Tedyoh, since you asked... the tompion's purpose was to keep dirt, dust, and rainwater from getting into the rifle's barrel, especially needed because soldiers always marched with the rifle slung over their shoulder muzzle-upward.