There is no specific legislation relating to 'high trees' but there is legislation in place relating to 'high hedges'. So, if the Leylandii are al individual trees, you can't fall back on the legislation. If though (as would seem to be more likely) then you need to read through this:
http://www.direct.gov...AndLitter/DG_10029999
You'll see that you'll need to pay a fee if you're to get your local council involved. My local council has this on their website:
"A fee of £350 will be charged to process any complaint regarding high hedges, a 50% discount is available for those on low incomes/benefits (subject to review)."
With regard to the tree overhanging a public footpath, my local council has never been slow to send me a reminder to cut back my Buddleia bush when I let it overhang the footpath! Their letters remind me that the law requires that overhanging trees and bushes must give footpath users (including stilt walkers, perhaps?) a minimum clearance of EIGHT FEET.
To find out who actually owns the house next door to you (hopefully with their address as well) click the 'Find a property' link at the top of this page and invest £4 in downloading the title register:
http://www.landregistry.gov.uk/
Chris