there are two issues
1) Planning Permission
2) Building Regulation Approval (Building Control)
- They are not the same thing...
The first issue is planning permission, which it seems you have quite a few answers on so I shan't say owt on that - don't know details anyway!).
The building regulation issue is simpler (for me at least):
From the photo's it looks like it is constructed of non combustible materials and appears to be less the 30m2 in floor area. Accordingly it would be exempt from the Building Regulations even if built close to the boundary - as long as it is detached from the house. If it is more than 30m2 floor area it would need approval. If it is within 1m of the boundary and built of combustible material it would need approval.
In any event the Council will find it very difficult to take enforcement action if you can show it has been built more than 12 months ago (injunction is a very very unlikely - though possible - option if the Council thought the building presented a significant risk to health and safety) -but it looks exempt anyway.
From the sellers point of view they can apply for retrospective planning permission which, perhaps, if the approval is straight forward might prove cheaper to them than discounting the price of the house (possibly) - I'm not that good on the planning stuff. They can also apply for a regularisation certificate for building regulation approval (provided it wasn't built prior to Novemebr 1985!) - although as noted above it would appear it didn't need this approval anyway.
Solicitors always ask (though often very late in the day!!) for copies of approval notices and completion certificates. If you proceed with the purchase this may well happen when you come to sell again so it is worth writing to the Council (Development Control - planning permission and Building Control - building regulations) to get a written response as to your legal position which you can keep with your deeds for the future. In terms of building regulations they can confirm that it didn't need approval. Include a layout plan with dimensions of the building and its relationship with the house and other buildings with your letter. Most will accept email for this (and may reply by email). It may be worth doing this anyway as a buyer to put your mind at rest.
Not so familiar with the planning process I'm afraid.
