If I go into a home, I will have no use for my house. My sons have told me that they are happy to stand on their own feet. If my house is sold to pay for my care, why not?
'Unfair council tax'? I agree that there would be fairer methods of local taxation such as a local income tax, but let's not go into that now. People living in rented accommodation also pay council tax. If they are on a low income, they can claim council tax benefit, as can owner-occupiers who are on a low income. If you think you qualify, ring up the finance people at your local council or ask Age UK or CAB for advice. Presumably you already have the single occupancy discount.
As for water rates, if you think you are paying too much, your water company will gladly fit a meter for you so that you pay only for what you use. I was quids in when I was living by myself in a four-bed house and got a water meter.