KURG have been working on a shaft in East Sussex near Burwash for a few years. This culminated in a determined effort to pump out the water flooding the bottom to see what was there. The photos are on their website.
http://www.kurg.org.uk/ Click gallery on the left side, look for the last image (Burwash pumping weekend) and click the image for a full gallery. Unfortunately I couldn't be there, but the level that was revealed answers some questions, and poses many more! The cost of the pump means that it is unlikely this will be repeated. The level is far too loose to be dug, and flooded up again very quickly after the pump was turned off. There is nothing like this accessible anywhere in the area. Dating is a problem but I suspect it is 1800-1900. (I know, that's a long period of time!)