There is a legal term that escapes me at the moment but probably has 'age'
in it somewhere which defines the parcel of land which is considered to be
part of your house.

Curtilage.

This should show up in Land Registry, title deeds, local plans.
If you extend your plot then this has to be registered on your deeds -
presumably this is where planning consent comes in?
This land is treated differently for planning purposes than agricultural
land. e.g. in most areas (but not e.g. in some national parks) you can
erect
a greenhouse, shed, summerhouse or similar without planning permission.
AFAIK you cannot do the same in the field next to your house - but then do
you have to get planning permission to put up a lean to shelter for your
pony?

As usual - no clear logic to anything.

Many greenhouses and sheds do require permission. The rules are reasonably
clear if you bother to go and research them. A Practical Approach to
Planning Law ISBN 0199255954 provides a detailed explanation of the law with
many decided cases detailed. Many local libraries should have a copy.