The planning regs state that you need permission for a fence over 1metre in height next to a roadway, or over 2metres if it's a boundary between you and a neighbour. You can look up the finer details on the Planning Portal.
However, if you are storing expensive equipment, I would advise you to have something more substantial than a wooden fence. That may make it more difficult to see the equipment to the casual passer by, but you would be surprised how easy it is to see over a fence from a wagon, or a tractor, or even a Transit van.
We have twice had machinery stolen from what we considered to be a secure compound. The thieves merely cut through the fence. We have now planted a hawthorn hedge and built a mound of earth all the way round the fence so at least they cannot now just remove part of the fence and drive in.