In reply to balmybaldwin:
The following organisations are involved in cave rescue in the UK. Apologies if I have missed anybody.
The representative body is the British Cave Rescue Council.
http://www.caverescue.org.uk/
Irish Cave Rescue Organisation
Scottish Cave Rescue Organisation
http://www.scro.org.uk/
Cave Rescue Organisation (North Yorkshire)
Cornwall Search and Rescue Team
Cumbria Ore Mines Rescue Unit
Derbyshire Cave Rescue Organisation
Devon Cave Rescue Organisation
Gloucestershire Cave Rescue Group
Mendip Cave Rescue
Midlands Cave Rescue Organisation
North Wales Cave Rescue Organisation
South East Cave Rescue Organisation
South and Mid Wales Cave Rescue Team
Swaledale Mountain Rescue Team
Upper Wharfedale Fell Rescue Association
Caving skills also exist in some MRT that are not mentioned here.