Questions such as yours are regularly cropping up on AB now. In part its because solicitors are getting much sharper about asking these questions of sellers.
Firstly, this problem is your sellers - not yours. However it becomes yours if you buy the property without sorting it.
Secondly, once a construction has been there FOUR years, the Planning Department can never force the owner to take it down again. However, if Planning Permission should have been applied for at the time, the owner can apply for a Certificate of Lawful Development after the event to regularise the situation. This is much the same format as a Planning Permission and involves submitting drawings similar to a PP application, and a fee.
Thirdly, it is possible that the owner was able to use what are known as Permitted Development Rights to extend the house - in which case no PP was required. Suuggest you search for and read a previous AB question within the last month that dealt with a similar issue. It is up to your vendor to demonstrate to your solicitor/you that they did the right course of action at the time (ie. asked whether Planning Permission was required). Suggest you don't go to the Planners yourself.
Fourthly, irrespective of the PP position, this development should have had Building Regulations Approval. This assures that the structure was built to minimum standards of structural stability and insulation thickness for example. Building Control applications are dealt with by another dept. within the same Local Council. If they didn't get it, that's a different problem and you should now be asking for an insurance indemnity policy from the seller to underpin the failure to apply for the required Approvals. HTH.