[SM] I think it unlikely, but I don't know.
[C,R,B] Neither Holy, nor Roman, nor an Empire a dam, nor a quarry, nor a barrow.
Calling it partly man-made may have been misleading. A simple "no" might have been a better answer there also.

[C] Not a natural cave.

Yes, it exists on Earth today.

[CdM] Yes, a geographic feature!

[SM] There is one warning sign I imagine is likely to be there, but nothing like "DO NOT REMOVE".
[C] No current religious function.

[CdM] Something like, in the sense that it would advise caution. (I have not actually seen the place myself to see just what warnings are posted, and haven't found anything on Google Street View.)

[B] It is in England!