Nothing local springs instantly to mind as Lodge Hill is pretty flat. You'll probably have to travel a bit to find somewhere decent.
You are right about riding fat birds, just make sure they are ugly as well to get the full experience!
Depends what you call local, There are a number of trails around the Ashdown Forest area along with the North and South Down ways. Sevenoaks around One Tree Hill and also around Tonbridge near Merriworth Woods. To be honest there is probably better road biking than Mountain Biking around that area.