There are storage facilities at Thriftwood caravan park at the top of Wrotham hill. Otherwise I don't know. We keep ours in somebody's paddock, in Hartley. The only other place I know of is at Medway Marina.
I tried to post a link. I can't find it now but will keep looking. In the meantime look at this one:http://www.localsearch24.co.uk/kent/Caravan-and-Trailer-Storage-269
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.