SSSIs were 'invented' by the Wildlife and Countryside Act 1981 and 'documented' by the then staff of the national conservation bodies (i.e. quangos). In Wales that was the Countryside Council aka NRW now, and in England it was English Nature aka Natural England now. Every SSSI has a Citation document which describes it in general, plus specifically what is seen of value and being protected, i.e. what the so-called Special Scientific Interest actually is. There is also an official Map showing its boundary. There is also a Management Statement which sets out how the quango envisions its future. Finally, there is a "naughty list" of Potentially Damaging Operations which the landowner is not allowed to do without first consulting the quango for conservation clearance. WCA 1981 also set up the framework for National Nature Reserves (NNRs).
To be frank, the SSSI system relies on landowners being helpful and generous in their role as custodians of the future for nature. Therefore if some quango becomes heavy-handed or ill-judged as to how it projects itself to landowners then there isn't going to be much generosity or tolerance of officialdom in return. In England, Natural England has figured that out and consequently is being nicer to landowners and trying to get what it wants through mutual understanding nowadays. The former Countryside Council for Wales used to work that way too. I'll leave it at that.
Some 12% of Wales, thus one eighth of its land area has been scheduled as SSSIs which is nonsense. One in every 8 square metres of Wales cannot have "special" scientific interest, if any at all. Really SSSIs are in many instances Development Planning Control by another name. Practically all of Snowdonia, all the Brecon Beacons, all the Berwyns, and so on, are huge blocks of SSSI. Obviously land areas that big can only be "managed for conservation" through landowner goodwill. The public, walkers and cavers etc, have a quite broad ranging "right to roam" so they can come and go as they please on someone else's land without any contact between them and the landowner who is on the SSSI hook.
In Wales, there are several NNRs with significant caves including the Craig y Cilau NNR (which has Agen Allwedd and Eglwys Faen on it), and Ogof Ffynnon Ddu (which has OFD on it). As to you getting hold of official SSSI documents - that is not too easy and I'll set out the method for Wales in a future post. But to give you a sample, please see the attached PDFs for the Llangattock SSSI which includes the Craig y Cilau NNR. There are over 1000 SSSIs in Wales, most of which obviously don't concern caves as caves are quite rare and need a particular geology. All NNRs are SSSIs too.