Further to seamooses post..
Not tried all of these but I think the following should be ok:
Pikedaw Calamine Caverns.
Sell Gill Holes - dry way is ok, not sure to what extent wet way floods.
Alum Pot - main shaft.
Rift Pot - the one on the Allotment.
Large Pot - going to Arcadia/Colossus - should be ok.
Rowten Pot - the P-bolted route, ok if wet but parts could be a bit unpleasant if it gets very wet.
Jingling Hole.
Pillar Holes - the entrance areas are ok, the extensions they did a few years back I have no knowledge of how the rain affects that part.
Lost Johns Cave - Dome or Centipede - depends how wet it is though, the entrance passage could get somewhat sporting.
There is probably a few more than that, just can't think of any more at the moment unless you like small and rather obscure caves..