c. 1200, creulen, "to move slowly by drawing the body across the ground," from a Scandinavian source, perhaps Old Norse krafla "to claw (one's way)," or Danish kravle, from the same root as crab (n.1). If there was an Old English *craflian, it has not been recorded.
Meaning "advance slowly" is from mid-15c. Sense of "have a sensation as of something crawling on the flesh" is from c. 1300. Related: Crawled; crawler; crawling.
1818, "act of crawling," from crawl (v.). In the swimming sense from 1903; the stroke was developed by Frederick Cavill, well-known English swimmer who emigrated to Australia and modified the standard stroke of the day after observing South Seas islanders. So called because the swimmer's motion in the water resembles crawling. Meaning "slow progress from one drinking place to another" is by 1883.