From Middle English cokel, cokkel, kokkel, cocle, of uncertain origin. Perhaps a diminutive of Middle English cokke, cok, from Old English cocc (found in sǣcocc) -le; or perhaps from Old French coquille, from Vulgar Latin *cocchilia, from conchylia, from Ancient Greek κογχύλιον, diminutive of κογχύλη, from Proto-Indo-European *konkho.
From Middle English cockil, cokil, cokylle, from Old English coccel, of unknown origin, perhaps from a diminutive of Latin coccus ("berry").