The roots of the leylandii will be over your side of the boundary and the earth will be very poor and dry. Unless you are willing to improve the soil greatly then I suggest spray painting the remaining part of the tree green to disguise it or use pots/raised bed but since you need that space I suggest the spray paint.

Ah, the innocent Leylandii hedge! Before doing anything read independent (disinterested) advice such as http://www.which.co.uk/documents/pdf/the-law-on-trees-153989.pdf You may also find something on your local council's website.

Before massacring your neighbour's hedge, tell them what you're going to do and offer them the cuttings (which belong to them).
Is the fence on your side of the hedge? Is it a wooden fence? If so, why not just paint it a nice bright/light colour to reflect as much light as possible and use the dry area at the foot of the fence for the path to the shed?

Firstly I agree so why not lookup/contact your council to see what your rights are as 18ft seems an excessive height to me for what is after all a garden hedge?
I would caution against doing anything such as spraying because damaging/killing a neighbours trees/hedge may get you in to hot water even if they are in the wrong!
Speak to your neighbour after speaking to your local council - you never know they may agree with you and shorten/prune them etc which might reduce what you have to do.
Remember to take photographs showing the problem especially before anything is done,

Thank you for your advice.
I have spoken to my neighbour and found that he wants to protect his privacy. he doesn't want the hedge clippings so where I need access I have cut back my side and will shortly erect a 6 ft board fence. His side remains green so he is unaffected.
As more of my garden is brought under control I will continue to chop and cover.
Sorry for delay in thanking you. I was encouraged by your helpful comment.