Only if you can relate it to an existing dwelling house i.e. if you have an existing house you may be able to build a domestic extension within the exempted floor area limit.
No private citizen can develop any completely new fixed structure without planning permission where no recent history of a development exists.
Is there ever a situation where a certain land area is privately owned and planning permission is not required?
Are you asking is there a situation were planning permission ins’t allowed at all for ANY development. Then the answer is no.
There is exempt development but certain building work will require planing permission no matter what the status of the land.