Unfortunately, English ivy, poison ivy and weed trees will eat anything you try to plant. Will cover any shrubs or trees you plant. And glyphosate and digging up will take lots of repeated times, and lots of work, and you still may lose.... How badly do you want that open view? Since you have limited control over the property there, the best answer may be a fence, with a deep-dug barrier behind it. Like a foot down with sheet metal or treated wood, to block roots. And then a solid-ish fence. Once a year you may have to head to the far side and rip the ivies off that side of the fence. But any other minor incursions, you should be able to beat back from your side. Depending on where you are, you may be able to complain to the city/town/county, and have them help with the nuisance next door, either clearing it or helping to pressure the land owner. It's worth exploring....

I have got a wall about 30 yards long and 8 feet high covered in English ivy and 4 walls about 15 yards long and 2 feet high. The only time of year when I don't have to prune my English ivy is from late November to early April. It will quickly get away from you otherwise. It will damage brick masonry but it take a good while to do serious damage--15 years or more. It will take the whole wall over. The sun won't kill it. It is subject to powdery mildew which doesn't seem to kill mine. It is also subject to rust,which will kill some of it, enough to make swatches of it unsightly for a while in mid-summer. That problem seem to take care of itself once colder weather arrives. I tried spraying Bayer fungicide on it (which works great on blackspot on roses) but that did not take care of the rust. For what it is worth the Bayer also failed to remedy the rust on a couple of dogwood trees. It is, however, great on the roses! The ivy will collect a lot of pollen, dust, etc. in its leaves and at certain times of the year pruning it can be irritating.

You may want to think hard before planting engish ivy as it most likely won't confine itself to the wall but will also crawl all over the ground with dozens of feet of vine eventually invading everything in the area. They definitely do better in shade and may fry in hot afternoon sun (or better, if the stone heats up, it can potentially burn the ivy's hold-fasts). And yes it may damage the masonry - particularly if you decide to eventually pull it off. I have seen too many over the years have to repoint the stone after removing it (I grew up in a stone tudor) and it's generally a mess. I have had to help my mother pull and pull and pull and pull english ivy along the base of her 8ft stone wall at the back of the property (which has both english and boston ivy growing on it). You might do better securing a trellis against the stone and consider growing some climbing roses there or plant foundation shrubs. The sun would be conducive to roses.

I have a patch of 'Thorndale' English ivy that was pretty for years. But this year I discover it has grown up on top of itself quite deep, producing a thick base layer of messy brown stems -- and some of the leaves on top are brown now, too. I'm hoping if I cut it all back to the ground, it'll grow up again. Anyone know?