Hi Neil, and welcome to the forum - have you seen the
Croesor-Rhosydd mine trip article? Probably more similar to the things you usually get up to, but as Sarge says, not a huge amount of difference between the techniques used in mines and caves.
Many of the caves around here (Derbyshire) are a mixture of mined and natural passage, and you'll often find yourself descending minedshafts to reach natural passage at the bottom.
You can't be that far from the Dales, where there's plenty of great caves for you to cut your teeth on, but it's a good idea to buy a decent guidebook and heed the weather forcast as many of them can flood suddenly (ulike most mines) and the consequences of that are of course, not pretty.