You are never going to stop it without a good systemic weedkiller and your neighbour allowing you to get access to the whole ivy plant. .. Ivy has a bark on the stem and a tough waxy leaf. Most weed killers won't penetrate the stem and the leaf will just shed the weedkiller.
You need to damage the leaves by a crushing them and then do the same with the stems. Then spray the whole plant with a systemic killer. You will need to do this a few times over a month or so.. and you should only do it when the weather is dry. Damp weather in Winter is not the time to do it. Preferably when it's warmer.
The killer I have often used is called Rosate 360..
.. it is a systemic killer and seems to deal with everything.
As with any of these kind of products.. reads the instructions before attempting to use them.
https://www.ebay.co.uk/itm/Rosate-360-TF-Glyphosate-Weedkiller-1-x-1-Litre-Strong-Professional-Herbicide-CG-/252820061781?_trksid=p2349624.m46890.l49292