I thought I should help provide some current information on the beaches to the west of Dorset that I'm familiar with.
Firstly Cogden beach Near Weymouth, although it's listed on various websites, I personally wouldn't reccomend Cogden. The beach  is quite exposed so it's normally windy, it's a very popular fishing destination so although it is a big beach, many textile holiday makers use the beach as a dog walking spot.
Further west is near Axmouth - best approached from Rousdon estate, although the access is quite steep, it is theoretically possible to drive down the track and park in the shade at the top of the path to the beach. This is a really nice spot on the undercliff. The other access is from Axmouth itself, although it's quite a walk on pebbles through to boulders. Mind your ankles! If you access from Rousdon, the beach there is infact a bay, and with such limited access it has a very plesant feel - very relaxed, often used but very rarely busy. I've seen plenty of naturists using this beach. It also has some natural shelter at the cliff base (very little danger) should the sun get too intense.
Hope that helps