The only way to stop them chasing you (which they are doing presumably because you have told them you are the Executor) is either to pay the CT bill or to provide them with whatever evidence they require that there is no money in the Estate to pay the CT debt. Ask them what they need from you so that they can write off the debt. When someone dies their debts are not cancelled, they have to be paid out of their Estate by the Executors if there is money in the Estate to do that.
If your mother, at the time of her death, owed debts (including the Council Tax) that were greater than her assets then she has an "insolvent estate". Have a look at this advice on what Executors must do if an estate is insolvent. In particular the order in which debts must be paid.
https://www.bereavementadvice.org/topics/probate-and-legal/insolvent-estates/Normally when someone dies neither their family nor their executor are liable for their unpaid debts. But with an insolvent estate if you don't pay them in the correct legal order you, as executor, could become personally liable for her debts. (If you are the legal Executor or Administrator that is - I don't know what you mean by "executor by default". Did she leave a Will?)
First priority is to pay funeral and "testamentary expenses".
It sounds like any other debts (such as council tax) will be "unsecured creditors". Are there any other debts except council tax? If not, and if any assets of are less value than the CT amount owing, essentially everything she owned (once you have it in cash) you have to give to Wigan Council.
This page has template letters that might find useful
https://www.bereavementadvice.org/topics/probate-and-legal/dealing-with-insolvent-estates/
