Sandy, My information comes from Sail Away, put together by Eleanor Locke, Boosey & Hawkes, 1981/1988.
She gives 5 verses, collected in Calif in 1978, then quotes from Mary & Herbert Knapp, One Potato Two Potato, 1976. They in turn quote from "a 1370 ms of Piers Plowman. When Piers goesd to check on those who are helping him plow his half acre, he finds them loafing about, pretending to be crippled : Somme liede here leggie a-lery, as such losellis cunne. (Some made their legs crooked as such losers will.)" So no reference to beggars _ I invented that! Startling to find such a modern use of losers here too! Don't have OED to hand!