There's a place not far from here with ancient and now unused sewage tunnels that come from the big house like those.
The lack of height (assuming that there isn't four foot of stuff on the floor lifting the level up) would suggest that to me.
I won't say that you never get caves in sandstone as there are areas where its water or windworn and creates hollows and all sorts but proper cave tunnels are far more likely in limestone.
Consequently I go by the idea that if the cave is in pretty much any other rock than limestone its man made. Ones by the sea might not abide by that rule exactly but you get my drift.
Anyway, I reckon that if you got to the end of those tunnels you would find an old toilet.