The story
First appears c. the 17th century, either from crompid cake (“wafer, literally, curled-up cake”), from crompid, form of crumpen (“to curl up”); cognate to crumpled. An alternate etymology is from Celtic; compare Breton krampouezh (“crepe, pancake”) and Welsh crempog (“pancake”). The sense of a “desirable woman” is attested since 1936, possibly as Cockney rhyming slang for strumpet; alternatively, compare tart (“a loose woman, a prostitute”) (itself possibly Cockney rhyming slang for heart or sweetheart). Note that muffin has a similar sense, and that, in the 19th and early 20th centuries, Muffins and crumpets was a familiar street-cry in the UK.
Etymology from Wiktionary, CC BY-SA 4.0.