Hi Saffyem and welcome to the forum.
The legal definition of "agricultural land" allows for a number of activities, other than just grazing or annual "farm" crops, and includes, for example, horticulture, woodlands and allotments. (The legal definition of "agriculture" is different though: for instance, horticulture is not "agriculture" - I mention in passing as I found it all a bit confusing at first).
If your use of the land falls under the accepted uses of agricultural land, there will be no need to seek planning permission for change of use.
You cannot, however, extend your private garden into a field next-door to your private home: that would be change of use and you would be given a good going over by planning authority if anyone brought it to their attention.
If planting tress; in some instances you need a preliminary Foresty Commission impact assessment. I can't remember whether there is a threshold for acerage, but I had to seek their assessment when considering planting 5ac of Christmas trees. FC decided my proposal did not require a full Environmental Impact Assessment (ref EU environmental legislation). I can't imagine 1ac of trees would twitch anyone's goat, but you might want to check out Envir' Agency or Forestry Commission guidance (or ring them) before planting other than a few hedgerow trees.
No doubt others with a better grasp (or better memory) of finer details regarding change of use will come along with comment idc. In meantime, I'll leave you with this: I knew I would need planning permission for new storage facilities, but I made a "Do I need planning permission" submission to Cornwall Planning, outlining my proposal to convert pasture to horticultural use (a tree nursery business with other agri'/horti' bits and pieces added on) to substantiate the need for equipment storage etc, just to see whether there was something I might have overlooked. Very surprised, I received notice that it amounted to change of use which would, in itself require PP. I contested the latter (being fairly confident the "advice" was incorrect), but received no reply. Slightly doubting my position, as a result, I submitted my full planning app': nary a mention was made of change of use during subsequent discussions or in the eventual notice of approval!