Are you hoping to hide the Leylandii? At 40 foot tall, that sounds an impossible task. I had a Leylandii which had been planted before I took over the garden, and which was nowhere near that height. Nothing grew beneath it, and evetually we had it cut down. A ground cover plant such as Vinca would fill the gap, as might other shade-loving plants.

These 40ft Leylandii are dry in the centre, and can catch fire. Your neighbour may need to ask the Fire Service for advice.

Its not funny Snoop, some boys set one on fire at the end of my garden, terrifying. Fire brigade were 20 mins getting up here. Police and neighbours helped. The fireman told me about them being 'as dry as a tinder box in the middle' - burned half my garden. It was awful.
The thing is if this happened to the one in the photograph you could lose your fencing and plants. I had a lovely
Acer - couldnt get near it to move to safety.

That looks like a very good example of a high hedge - a row of two or more evergreens. Have you asked the neighbour to cut the hedge to a more acceptable height?

as to what will grow.... Not much! If you have the money I think I would build a high wall (unfortunately you won't be allowed to build a 40ft wall) with a raised border in front of it and extend the paving - put a patio on that side of the garden and flowerbeds/border etc where the paving is now. Then have lots of big pots on the patio.

First thing though would be to get that wall of darkness reduced - I shouldn't think it was doing very much for your mental wellbeing facing that all day, every day.

we had kids burn 2 of these trees and they roared away violently . its not funny . I mite just ask the nieghber there feelings on this tree as they will have the same problems and may want it down . you could put a nice water feature in there if not with decking etc as mentioned .

Thank you everyone for your suggestions, much appreciated. The leylandii was like that when I moved in. Dianabulley and Snoopdog, thats very naughty. Will be moving my shed out of range in case of a fire next week as the middle of the thing is extremely dry and you can't be too careful can you. Would love a patio there but its the one part of the garden that gets hardly any sun. Melchisedec, will look up Vinca's. Now I have the roots on my side exposed might chop them and put lots of weedkiller (hopefully highly flammable) down. Thank you again for all the advice.

Be careful what you wish for, Dogsallowed! You sure don't want a tree that size to go up in flames!

your welcome dogsallowed

Saw the most beautiful garden a little earlier, walking the dogs in the wood, the bluebells were out, lots of other flowers and everything was coming to life. My idea of the perfect garden and its maker the perfect gardener.