Claiming Council Tax Benefit

Hi, everyone, I am looking for advice on how to claim Council Tax Benefit as my financial circumstances have recently changed. This being all my savings have been used up and now I am living on my ESA, PIP, IIDB and a very small monthly pension. I have also had to take out a 10yr mortgage to add this to my savings and pay this as a settlement payment to my ex-wife. Now due to this, I applied for Council Tax Benefit on-line and completed all the information requested, and within 3days had a refusal letter from the council tax benefits office. I enquired as to what the problem was and I was told that they could not see how much my IIDB was and could I provide them with any proof. I called to the offices and gave them all of my awards letters from this years increase letters from ESA, PIP, IIDB, and my P60 for the small pension increase statement. They took copies of everything and said they 'd be in touch. Move on 4 weeks and heard nothing so I telephoned to ask what was the situation and for an update. I was told that they had not yet had chance to look at my application but not to worry as any award made would be backdated to the date of application, and I was to wait a while longer. Move on 3 weeks and again heard nothing, so once again I called the office concerned for an update, to be told by a rather abrupt lady that a decision had been made and refused. On what grounds I asked? Because I earn too much, was the reply. I do not work anymore due to my disabilities and live on benefits and little pension was my reply, how can I earn too much? Well your income is too high to qualify for any award, she said, and if I don't agree with the decision I was to wait until I received a duplicate copy of the original letter that was somehow mistakenly never sent out to me in the 1st place and write back in to appeal this decision. My question to my fellow members is for any advice on how to deal with the Council Tax Benefit Office and if anyone knows exactly what the criteria is for claiming this benefit? Because as to my knowledge it says if you have less than £16,000 in savings you can claim, if you are out of work and claiming ESA, you can claim, if you are disabled, you can claim. As far as I have seen, never ever or anywhere does the application forms state or intimate that this benefit is based on earnings/income, but purely on savings. Can anyone on the forum please advise me on this, and indeed as what to say to the council or do in response, please.
Many thanks everyone, .....Moose