We had a similar problem.
I hacked the trunk through & removed what I could from our dry stone wall without pulling it down. I then drove as many copper nails into what remained of the Ivy in the wall. As far as the trunk went, I bored a hole in it & filled it with root killer. That was about 4 years ago, & touch wood, it hasn't come back.

Hi, I found an Ivy killer spray by Growing Success Organics Ltd. It was systemic so killed the roots as well after a couple of applications. I think it was reasonably priced measured with the 'Killing success ' it had :D