What is the cave called in the peak district in Derbyshire?

There are many caves in the Peak District, such as Peak Cavern (aka unofficially as The Devil's Arsehole), Blue John Cavern, Poole's Cavern, Speedwell Cavern.

All are well worth visiting.

Speedwell and Peak Caverns are in fact linked, but in a remote region beyond the show-cave limits.