You may know this but I had missed it until someone came to help me with some other forms for Mum.
Under council rules there is a Council tax discount/exemption for the severely mentally impaired which includes anyone with a dementia/Alzheimer's diagnosis. If you put "Council tax discount/exemption for the severely mentally impaired" and the name of your council in google you should find out about it in your area.
A diagnosis should mean the person is exempt from council tax. This makes a spouse, in effect, a single council tax payer so they would get the single discount of 25%. A person living on their own should get complete exemption. If other people than a spouse are living in the house there may still be some discount.
we really do need a middle of the night moderator