I've heard that dehumidifiers aren't good for chest probs too, however in this case as it's only a short term thing... does the benefit outweigh the risk? If the wall doesn't dry out quickly it may go mouldy and I suspect that could be much worse for you.
Maybe your local pharmacist could advise, or you could call your GPs reception and maybe speak to the practice nurse.
I've no idea about the electricity, perhaps your HA has an advice line (I know a lot are absoloute rubbish to deal with)...maybe they could give you a small grant (I dunno if you have a key/card meter or pay by DD) or credit your key with a fiver or something? It's not something I've ever heard of but still could be possible.
Opening your windows and turning the heating on may work but again that's going to cost you in heating expenses...plus our good old British weather being as unpredictable as it is...it could end up chucking down with rain and undo and drying you'd achieved.
I dunno if any of that is any help, just thoughts off the top of my head....oh and it's just started belting down here. Typical!