In reply to Jerry67:
You could try Swanage Bijou Camping on Victoria Avenue.
It's pretty basic and, while not self-contained, the wash block (and I use the term extremely loosely) is basically a few sinks on the side of the main building and is as open to the elements as it is possible to be.
Therefore, it is about the only one I can think of that would have a chance of opening.
Edit - there's a picture on Google that gives an idea of the facilities.
Post edited at 10:43