Hi Claireylouise - it's hard to eliminate marestail completely and even more so if it's coming through from your neighbour's garden, as any effort you make on your side of the boundary won't stop it growing there. I'd suggest that whatever steps you take to kill it off, you ask your neighbour if you can do the same on their side - otherwise you'll have a never-ending battle. If you google for ideas as to how to eliminate it, you may well find suggestions that you use glyphosate weedkiller. This will work OK, as it travels to the roots and more or less kills stuff from the roots up. However, this particular weed is a somewhat tough & even "waxy", so to get the glyphosate to work you need first to bruise the shoots (using gloved hands) so that the solution is taken into the plant - otherwise it'll just wash off in any rain. You have to be very careful not to let the weedkiller touch anything else - or that will die too. I'm so glad I don't have to deal with it & wish you lots of luck!