Our second house had a line of eight Leylandi in the front garden. They had grown to about 14 feet and needed seeing to. I lopped them to six foot, but then they became 'thicker' with foliage. I eventually hired a chainsaw and took them right back to ground level, then drilled the stumps and filled them with root killer. Best thing I ever did.
Lissie, I am thinking that you be sick of their new look after a while and might go the whole hog and get rid completely.