Landlord not passing on cost of living rebate

unforeseen

The tenant is the person responsible for paying CT. If the LL does not pay the council then it's the tenant that ends up in court with no defence.
There is a strict liability order for the person responsible for CT and the LL isn't one of them (ignoring HMOs).

At a guess the tenant has probably been told not to register themselves on the electoral roll either. 

macman

jj_43 said:

The council tax is included and payable to the landlord (it’s a service charge), there are many reasons why it could be done in this way. Not sure what the extra admin would be? Having the bills in one name consistently is actually less admin than notifying the council between voids. Not sure what’s to conceal here, having a council tax in tenants name does not identify a property as landlord. 

Because it's indicative of a rental where the landlord has illegally subdivided and not registered the unit as a separate dwelling. LL's who do that usually aren't declaring the rental income either, supplying GSC's, or any of the other myriad requirements of being an LL.
We have no way of knowing if he's passing the CT on or not.
OP needs to check if the property is registered, since they are still liable for any unpaid CT.