If you'd like to hike along the coast here best go to the National Trust site for information. The coast is erroding as shown by this pictures of the demolition of the old coast guard station at Birling Gap: England's vanishing coastline.

If you're curious about the term "Downs", Gwen Jenkins provided this explanation:

"Downs" is a geographic term. "Down" was the Old English word for "hill." It served for "up" as well. Our word "down" comes from the OE practice of forming opposites by tacking an a- on the beginning of a word, in this case forming "adown." Eventually, the a- was dropped. Another example of this development: OE for "stay" was the root we get "leave" from (so it must have been "aleave" at one time); our word "love" derives from the same word, which I think is interesting. The Downs are fingerlike because these specific hills are evidently "coombes" (the welsh word is "cym," pronounced pretty much the same way). Coombe Tracy figures in The Hounds of the Baskervilles, and you'll notice a lot places named Combe or Coombe on the map. These, I've recently learned, are U-shaped hills curving around a little valley, sort of like box canyons, or the cells in honeycomb or the fingers of a comb.

On the Ordnance Survey maps the topography is shown and one can see the fingerlike hills pointing down to the sea, forming valleys.