Extract from Burgess’s 1960 novel The Doctor is Sick (p. 100 of the Penguin edition):
That word you used has a most interesting history. You find the Middle English form coynte. Earlier forms have a more definite initial kw. Cognate with quim, of course and also, not perhaps as surprisingly as you might think, with queen. The quimtessence of womanliness, you might say.’ He was pleased with his pun, but nobody seemed edified or amused.