Simple answer - you cannot legally build any sort of structure to live in on any land without permission - be it yours, someone else's, farmland or yard. Putting a house on land constitutes a change of use and for that you need planning. You will not get permission to put a house/caravan/shipping container or any other sort of proposed habitation on just any land merely because you own it. The reasoning being that if this were possible then our green and pleasant land would soon look like some haphazard shanty town.
Under the 28 day rule you could certainly build it, if you could do it in that time. But then you would have to move it somewhere else every 28 days onto a fresh piece of land. So it is not likely to be feasible.