Martyn Farr runs cavern or intro courses in Ireland if there's numbers to make the trip over worthwhile. Don't think he's been over for the last couple of years. Doolin is the best place for cavern but it's next to impossible to plan a weekend down there weather wise. Martyn is based in Llangattock in south wales with access to a good variety of training caves / mines. If you can sort out cheap flights to Bristol, it's only a hour and half drive to his place.
Matt: There's no such thing as "cavern" in Ireland / UK

Cavern strictly refers to diving within the cavern zone of a cave, which is the section that natural ambient light reaches. The cavern zone in most irish caves is probably 2m. Even in doolin with great vis, you're doing well to have ambient light beyond 15m