What's That Then?

I've been deeply immersed in the Romney Marsh this week (and once or twice quite literally), but obviously couldn't resist another flying visit to Dungeness. On leaving I spotted this curious building, looking like a 1930's public lavatory for the vertically-challenged. But I know that the Southern Railway ran trains down here until 1937, so wondered if this was something to do with it. It's so out of character, that is: not being made of driftwood and not looking like it might take off in the next Channel storm. So, can anybody out there help?