Here's a very early mention of "Souling"—from a commentary on Shakespeare from 1788:

It is worth remarking that on All-Saints-Day the poor people in Staffordshire, and perhaps in other country places, go from parish to parish a souling, as they call it; i. e. begging and puling (or singing small, as Bailey's Dict. explains puling) for soul cakes, or any good thing to make them merry? This custom is mentioned by Peck, and seems a remnant of Popish superstition to pray for departed souls, particularly those of friends. The souler's song in Staffordshire, is different from that which Mr. Peck mentions, and is by no means worthy publication. TOLLET.