Can I use this as an opportunity to mention that people with what is described for council tax purposes as Severe Mental Impairment (which includes some sorts of learning disabilities and some sorts of mental illness) can get a complete exemption from council tax.
There are limits on how far back you can claim council tax benefit, but if you apply for it and don't get it, or get the wrong amount, because of maladministration, you can claim compensation to cover your losses.
Councils can go back many years trying to claim council tax and at the CAB I've come across some horror stories. My local authority even tried to argue before the magistrates that someone's Post Office receipts had been provided improperly by the local Post Office. When the court threw that out, they asked for extra time to dig back further into the past. So it's well worth getting extra help if the council gets awkward.