An Annex can be charged separately, depends on the use.
We had a Council Tax W exemption for Dad, as over 65 - Annexes lived in by dependant relatives (class W)
If you live in a property split into more than one home and are a dependant relative of someone living in the other, you don't have to pay Council Tax.
The most common example of this type of property is a house with an annexe.
To qualify for this exemption, it must be your only or main home, and you must be one or more of the following:
aged 65 years or more
severely mentally impaired
substantially and permanently disabled
you must also be related to the person that you depend on.
The property is sadly now empty, there is nothing to pay but early on, after the first resident of the annex died, the couple here at the time did let it out, and that meant it was subject to council tax, even though it totally depends on the main bungalow for all services.
Our annex has no separation for any services, so water, sewage, heat, electricity are all connected and as we had one shared phone line (at the time), shared aerial, also not subject to separate bills, so cannot operate as a separate dwelling or be sold as one, but still has a potential charge against it and we receive a nil bill, as per the exemption each year.
Our local council also checks every year to confirm that it is still empty, so, if they could charge outside of the exemption, they'd be on it!
www.gov.uk/council-tax/who-has-to-pay