If an annexe is a self contained unit, it must be treated as a separate dwelling under the Council Tax (Chargeable Dwellings) Order 1992. Conditions attached to planning permission that prevent a separate sale are ignored as all dwellings must be banded for council tax purposes using the valuation assumptions set out in regulation 6 of the Council Tax (Situation and Valuation of Dwellings) Regulations 1992, which include an assumption of sale.
The addition of a conservatory is likely to be value significant and would constitute a “material increase” under section 24(10) Local Government Finance Act 1992. As such it would not affect a council tax band unless and until a “relevant transaction” took place (and only then if it added sufficient value to put a property into a higher band).
In the event of a revaluation the existence of a conservatory would be taken into account, as would any other feature, positive or negative, that affects value in the market at the time.