If the barm were for agricultural use then you'd look at the rules for permitted agricultural building and that would lead you into what permissions you would need to apply for, or whether you would only need to notify your intent, giving the council 2 months to object if they thought you needed to apply for permission.
But you are proposing to take graded agricultural land and use it for another purpose, which would require change of use, i think. And then the permission for the building relevant to the new categorisation of the land, I assume.
There is no permitted development for an agricultural building on holdings of less than 12 acres.
However woodland on the other hand
does have PD, with no minimum size. The building just has to be used in connection with maintaining the woodland. You could therefore, using permitted development, build a barn to say - house your equipment, dry the fire wood, fence posts, logs or whatever you could claim to be producing. Look up permitted development for woodlands and work out from that what you could say you need the building for.
Once the building is up, then unless you annoy the neighbours somehow and they report you, it is highly unlikely the planners will investigate the odd building course. If they do, then you can apply for planning for change of use of your building. It is always easier to get change of use for an existing building than to get planning in the first place on a vacant site.
I have done something similar by putting up 2 agricultural buildings on our farm with permitted development (I have more than 12 acres) and then applying for change of use to storage.