Mike, what a doddle of an install that would be! You could have the charger fitted either under the hanging basket, with the shed on the other side of the wall or have one fitted inside your shed, with the cable coming under the door (small cut out if needed) and run the cable down the side of the path. Another benifit of having the charger in your shed is because only 8 0r 10 feet of cable is needed, you could essentially hook it on a hook save winding it up!
I can’t see a close up of your meter box, to see the srating of the cut out (fuse) but the tails look right at 25mm2.