Hedges. These are not covered by planning permission so you can go to any height except the neighbours can take action using the high hedges regulations. Under these regs you might have to bring the height down to 6' 6" if the hedge is keeping light from neighbours house windows.
Fences. Up to any height if you get planning permission. Without permission you can go up to 6'6" except it is 3'3" adjacent to a highway. Adjacent is subject to interpretation, and in this case the definition of highway is any verge, path, or road - but their must be a road involved, not just a path.
The heights are measured from the land on the side of whoever puts up the fence, and it is the original land before any lanscaping or decking etc