cut the stems as close to the soil level as you can to prevent it continuing to grow on your side. In the past we have used a paint stripping tool / blade to prise the branches/stems off the wall. If done slowly it shouldn't do much damage if any. If the wall is in a poor state of repair you may need to go even more slowly. Just cutting the leaves off wont stop it continuing to grow.

I would go with Eileen and cut the main stems off at ground level. Then with a sharp blade cut the secondary stems at every four inches. Then leave for a couple of months so that the roots dry out and lose their grip. Then give the walls a good brushing with a stiff brush. This should deal with the most stubben clinging roots without damaging the wall.

hi many thanks to everyone who offered me their adviceuch aprecciatedy

I've used salt to kill off Ivy. Sprinkle liberally on the ground after cutting off the vines from the roots. Plain table salt works.

too much salt will prevent you growing anything else in that area, so proceed with care if you want to grow other plants there