People who occupy non-domestic properties such as shops, factories, offices and warehouses do not pay Council Tax on their property. They are charged Business Rates, otherwise known as National Non-Domestic Rates (NNDR).
Who pays business rates?
If the property is occupied, business rates (NNDR) are payable by the occupier. If the tenant of the property is paying an inclusive Rent & Rates payment to the landlord, the tenant needs to make sure the payment of the rates gets to the council - if the landlord does not pay the rates to the council then the tenant will be pursued for the payment using all recovery methods available to the council.
The council cannot legally enforce payment of rates against the landlord in these circumstances, regardless of any terms in your lease / rental agreement; you would be pursued by the council, you would then need to reclaim the rates from the landlord.
If the property is unoccupied an Empty Rate is payable and liability rests with the owner of the property. In this case, the owner is regarded as the person entitled to possession of the property, this includes the current leaseholder.