It looks like the conifer Chamaecyparis. They are usually good as a hedge and respond well to clipping. They should be trimmed, like a hedge every year in September, thats if you want a hedge. If not then they would have to be taken down and the roots dug up. It looks as though next-door's have some sort of climber coming over. Good luck.
You should join GoY and then you could show us your Before and After photos.

Looks like leylandii to me - cupressus leylandii, but a close up showing the foliage clearly would be useful to be sure. If they are, they need to be pruned every two years minimum, top and sides, or they'll be 50 feet in no time.

Thanks for your help. I have 2 suggestions - Chamaecyparis or cupressus leylandii. I'll take some photos of the foliage when the weather improves and post them over the next couple of days.