If the ivy roots are in your neighbour's garden then technically it's their plant. You need to warn them if you are going to use glyphosate because you are likely to kill the whole plant.
They may be fed up with it as well though 
WORD ASSOCIATION -27 (June 26)
) is to keep cutting back and spraying. We've got bindweed and ground elder as well. You could try covering some of it with a plastic bag and lightly crushing the leaves, then spraying inside the bag - to stop it getting washed off by the rain! Lightly crushing the leaves will help the spray get into their system, as Ivy's leaves are pretty impenetrable! Good luck 
