Your not doing any structural alterations so you do not need to contact your local authority building control office...
I think the above is how the Law is currently, whatever the planningportal guide or LBO might say, remember their advice has a disclaimer.
A friend of mine had a LBO tell him that if you built a brick outbuilding (smaller than the 15/30m3 BC limit) as soon as you incorporated some insulation, then part L applied! The officer also said something like.."the question arises as to why you would want to insulate an outbuilding??". The answer of course is: insulated outbuildings do not cook in the summer and freeze in the winter, items stored in there - paint for example, last longer, chest freezers like them, and if you want to use it for a bit of DIY its a joy to use in the extremes of weather. My friend didn't bother giving that answer to the BCO, is was not worth wasting time to reply.
I have found LBOs do vary. Not all go in for intimidatory tactics.