... turn a pathetically small patch of grass (2m x 4m, maybe less?) into either a tarmac/gravel/paved driveway - I wouldn't need a drop curb because we already have one it's just extending the side of our driveway?
From what I can remember reading about this a few months back, as long as the end result is water permeable (so gravel or similar) then you can do what you like. You need planning permission if you increase the amount of impermeable surface on your property, because it will potentially increase load on the existing drainage system
You will not need planning permission if a new or replacement driveway of any size uses permeable (or porous) surfacing which allows water to drain through, such as gravel, permeable concrete block paving or porous asphalt, or if the rainwater is directed to a lawn or border to drain naturally.