http://rnli.org/NewsCentre/Pages/Injured-man-rescued-from-cave-by-St-Agnes-RNLI1.aspx
This was presumably from Towanroath Cavern

Previously heard of a caver falling off trying to climb up the difficult climbs out of the cave (pitches unless you are a good climber) & breaking an ankle, having been cut off by the tide (which is probably even easier to do now lots of the beach disappeared in the winter storms).
A rescue would be possible through the pitches/traverses in the cave, but not sure of the Coastguard are trained for anything involving more that direct pitches.

I've contemplated climbing the wall of the sea cave out to daylight via the cut miners "steps" but never attempted it as it appears to be far too slippery.

The only thing I have done is dived into the cave - not a cave dive obviously as not an overhead environment. It is quite pretty diving around there and there are some interesting submerged caves on the other side of the cove.

Met one of the lifeboat crew the other day, who is also a caver. Apparently the casualty fell from the top entrance of the cave, ending up on the floor - that must be a fall of perhaps 20m or so - breaking his ankle in the process. He attempted to freeclimb the bottom pitch - difficult without a broken ankle - and fell off again, so retreated to the back of the cave. Conditions were unusually calm, normally it would be impossible for the ILB to get anywhere near the entrance.

He was very lucky to escape in one piece!