@alphabeta,
Is this council tax a tax on a residence - in other words do all residences pay some sort of council tax.
If so - you also own a business. The business profits from things like good roads (so customers can drive to your shop for example) - a business also uses public facilities.
A business and residence are two separate entities even though in a sense a business owner may be a resident and a business but both of these entities benefit from public facilities separately.
I am not against each (even if it is one person) getting charged a tax/fee as I see the two as separate entities.
I am not sure what sort of business you have so making an assumption that you have a physical location for your business - you are using roads, public lighting, police, fire, etc for your business. When you close up shop for the day and go to your residence you again are using these public facilities for your residence. On top of it your business is profiting from using these public facilities.
The only issue I can see is if this tax/fee is fairly charged.