Do you have any written agreement with the council regarding this?
But clearly you can demonstrate by bank statements what you have actually received - have you shown this evidence to the council to establish that a deposit or a months rent has not been paid.
I must make you aware of a potential banana skin. If a landlord fails to register a deposit with the tenancy deposit scheme it can be sued for 1 to 3 times the value of the deposit. I am not sure based on the above if you have registered the deposit as you never actually received it. Potentially you could be sued by the tenant. Of course this is if they claim that a deposit was in fact paid to you.
The issue with registering the deposit late still leaves you exposed to a potential claim. It has to be registered within 30 days of the start of the tenancy.
Furthermore because the deposit has not been registered or if you register late then you cannot evict the tenant using the s.21 notice. It will be invalid. You will have to go to court to evict the tenant. The second issue is that you have to refund the deposit before you evict, otherwise it is invalid.
You can register the deposit late. You are still exposed to a potential claim. Give details to the tenant.
The council pays in arrears. Does this mean they will pay at the end of the tenancy for the last month
Not normally but you do when it has not been registered.
Their claim is that you do. Now it would be a case of the court, if it went that far, to establish whether or not it was paid.
It is too late to take the stance that there was no deposit and never asked for one, unless you have actually never asked for a deposit or at least not in writing.