We seem to have flown miles away from the topic of recreational access rights in the C19.
Regarding NRW and Natural England and Defra claptrap about 'caving' not being an 'open air' recreation: the earliest political references to ‘open air’ and ‘recreation’ were in Parliamentary debates on the 1845 Inclosure Act, unless you know better. The same debate later referred to such as ‘exercise and recreation' implying they were the same thing.
Enter James Bryce MP:
• He introduced the first Bill for a "Right to Roam" in 1884
• It failed
• He introduced a Bill again every year until WW1
• These failed every time
• British Ambassador to USA 1907-13
• Later became First Viscount Bryce
Unfortunately Bryce died just before his right-to-roam vision became law in the 1922 Law of Property Act. Its 1925 version was a "tidy up" and is still on the statute book. Section 193 gives public rights, as distinct from commoners rights, to take “air and exercise” over Metropolitan and Urban commons which includes places like Ogof Draenen both "above ground" and in places "set apart from the surface" by virtue of the very broad definition of "land" within the Act, at section 205, as including "any strata or seam of minerals or substances in or under any land" as open access land.
The "open air" term returned after WW2 in various National Parks Acts to the future delight of those lovely people at Defra etc who wish to portray caving as an indoors activity like ballroom dancing, and not as an outdoors recreation, for the purpose of depriving caving of its statutory access rights as suits their private agenda.