Full council tax demands due to being a carer

Birmingham City Council are charging me £145.85 per month for Council tax because they have decided my carers allowance is classified as working for the purpose of Council Tax. I have been forced to hand over this money or face an extra charge of £75.00 of Court action. They are telling me if my income is over £550.00 a month they will charge me full council tax. In effect they are taking my carers allowance for payment. After paying this I cannot put my heating on at all. Any advice would be helpful please.

Talk to the Carers UK helpline.