Firstly I'd approach the neighbours - they might be quite willing to do a bit of pruning, particularly if you offer to do/pay for the job. Secondly if they are not willing to give the trees a trim and you really want to buy the property go ahead buy it and trim the branches overhanging your boundary and offer the trimmings to the neighbours and as Marley says plant clematis montana. They neighbours can chop it at will but it will grow back just about as fast as they can chop. Pruning as you describe will certainly not kill the trees, but will leave voids - but those of course could be filled with clematis.
Marley, that is a GREAT idea. Hadn't thought of it, thanks. Chop my side, hide it with a tough climber. Maybe an evergreen though - even Ivy! That'll learn em! I'm sure any conifer will die by cutting back so much old wood, though.
"I'm sure any conifer will die by cutting back so much old wood, though." I still disagree. If you cut the trunk off at the base yes. Cutting ALL the branches off on one side, no. Might make them prone to fall over the other way in a high wind though - no idea where the libability would lie for that. And if they did die as a direct effect where would the liability lie for the cost of their removal? IMHO you are going about this the wrong way, but its up to you at the end of the day.
I don't think they would die either. What is the name of the method of pruning these sort of trees, into a hedge like shape, with the trunks bare (branches removed) up to a certain height, then the foliage allowed to grow into a hedge? I've seen it done rather successfully, but can't remember the name. Surely this is similar - removing part of the tree? Whether it is the side or the bottom would be immaterial. Wouldn't it?
Here's a Revived Leylandii Hedge I saw on my travels: http://kgarden.wordpress.com/2008/11/27/reviving-a-leylandii-hedge/
And if they did die as a direct effect where would the liability lie for the cost of their removal? Good point Krisin. I have no idea. I know I'm allowed to chop my side, but no idea if that makes me liable if the thing dies. Can anyone help with this? Btw - Plan A is of course to chat to the neighbours and HOPE they are nice and accommodating. I'm just bracing myself for Plan B. Aaron - that involves gradual pruning and clipping though, not removing a mass of old wood all in one go (this is another sketchy recollection from college btw - I'm sure my tutor mentioned one-third old wood as the fatal tipping point for conifers)
I was using that idea (and I still don't know what it's called!) as an example that they wouldn't die, not that you should do it. Good luck with Plan A. Fingers crossed they are accommodating.
Andreh, maybe you better hope the connifers don't die if you cut them. You are entitled to cut anything which overhangs your property but you are not allowed to damage the trees. It's a fine line.
Dunno how the ones in my link were done, but if it was all-in-one-go it was brutal, and they certainly didn't die!
There are conifers and there are conifers, maybe a mature pine tree cut hard back would die but I cant see leylandii doing the same. Are the trees on the sunny side of the property. ie south or west, creating shade. If not, its not a problem, if they are blocking sunlight then you may need to do something, but to actually go speaking to the neighbours before you even own the place seems a bit pushy to me, and might get a poor response.