Jinster2 It sounds as though you are in a very similar position to me.
If you're receiving the new full state pension, it's unlikely you'll receive much help with your council tax. I expect you've already worked out how much help you can receive with your rent, based on your local housing allowance.
When I first applied, I had to provide three months' bank statements (as Elowen33 wrote) and I wrote a note that my income was due to stop. I was self-employed and it was during lockdown, so my work just dried up overnight. At nearly 70, I think you have a very good reason to give up work and (hopefully) you'll be believed.
I'm afraid I did have to wait a few weeks before I was paid anything, so you might need to grit your teeth (and tighten your belt) for a while. When it was worked out, the payments were backdated to the date I first applied, so it's worth applying as soon as you can and state the date you are giving up work.
Hopefully, they will reply soon to let you know what's going on. If you're absolutely destitute, it might be worth asking if you would be eligible for some kind of crisis loan, which you'd have to pay back, but at least you'd have some money to pay your rent, etc.