Fascinating tool. OK, this is the beta edition. The first thing to do is differentiate the opacity of the layers showing Common Land and CROW Access Land which by default draw in the same shade of green so you can?t tell them apart. You also need to reduce the opacity of ?urban common? way below 100% grey (the default) otherwise you can?t read the underlying map which unfortunately isn?t either the OS 1:50000 or OS 1:25000 so a lot of useful annotations like ?pothole? are missing.
Having adjusted the settings as above, you can see that most of Mynydd Llangattock and land over Ogof Draenen is ?urban common?. This means that this land isn?t CROW Access Land governed by the CROW Act 2000 but instead is governed by the Law of Property Act 1925 regarding recreational access rights which are broadly ?air and exercise?.
NRW?s position, not supported by any external legal advice, is that caving is a form of ?air and exercise? but common land doesn?t include caves on common land. This is despite the definition of ?land? in the LPA as ?including mines and minerals, whether or not held apart from the surface?. LPA doesn?t mention caves, but the general idea is that common land includes the 3D and is not restricted to the 2D surface. Limestone from a legal viewpoint is a mineral.
Caves on urban common include Agen Allwedd, Eglwys Faen, Pen Eryr, Daren Cilau and several Ogof Draenen entrances. Make your own mind up.