Advice please

I am unwell and am on ESA support group and have also recently been awarded PIP. My husband has just been accepted as a carer which is a huge relief to us as we both suffer from ill health and dont know how we would have managed.

My question is we receive help with the council tax as we are on low income and have a little savings - just under the £6000 limit to receive this.The carers letter says we may be entitled to a back payment as we applied the beginning of feb and it has only just been dealt with. If we receive the back payment it will take our savings over the £6000 limit and im worried this will effect our council tax reduction. Has anyone had similar please? They very unfairly state that the money in your current account is included in the £6000 total which is mad because nearly all that comes in just pays the bills!

From the above link …

If your savings are:

under £6,000, your benefit claim is not affected by your savings
between £6,000 and £16,000, you lose some of your benefit payment
more than £16,000, you’re not eligible

Every £250 over £6,000 counts as if you had:

£4.35 of monthly income for Universal Credit

£1 of weekly income for Income-based JSA, Income-related ESA, Income Support and Housing Benefit
I’m almost sure the levels apply to council tax.