First of all, separate the Planning from the Buildings Regs.
Planning: the only way I can think that the council are accepting this situation is that it has been constructed using Permitted Development Rights. These allow householders to extend their property, or build a structure in the garden. For your house, PDR would be up to 15% of the VOLUME of the original house or 70 cubic metres, whichever is the greater. PDRights do not (normally) exist in Conservation Areas, National Parks or other special areas (AONB for example). If this structure is within PDR, Planning Permission is not required - ask the seller.
What PDR do not usually do is allow one to build a separately assessed (Council Tax) extension - as you say you have here. Very odd.
Building Regs: treat these as a separate matter - they ensure the structure is built safely and to minimum insulation stds. Wooden structures is not the issue - there are plenty of wooden houses around. Insulation and fire safety stds certainly are. Without BR approval you have a storage space and the space is regarded as non-habitable space. This stops the vendor calling it an extra bedroom. As non-habitable space, I cannot understand how the council could regard the annexe as assessable for Council Tax - its should be just a storage space and I do not believe one pays extra CT for a large shed. It is my guess that the CT people do not realise that it does not have BR approval.
Is it a problem to you? - probably not. If it has been constructed using PDRs it is perfectly legal. Can anyone sleep in there? - not really, but its not illegal unless you were renting it out.