"small thickly wooded valley," from Old English denu "valley" (see den). Confused in Middle English with den. In Middle English down and dene meant "hill and dale."
"bare, sandy tract by the sea," late 13c., of uncertain origin, perhaps connected to dune, but the sense and the phonology are difficult. Related: Dene-hole (1768) "ancient artificial excavation in the chalk-formations of southern England." By local folk etymology Dane-hole, and reputed to be where the vikings hid their treasure, but there is no historical evidence for this.