I'd be interested to read any replies on this question as we have next doors ivy 'invading' our garden - under the fence and over the fence. It's a never-ending job, I just keep on cutting it coming over the top and snipping the roots under the fence.

I gather that a brushwood killer, e.g. SBK would kill it, but you'd have to protect any other plants including shrubs that were within range.

I would contact the owners of the property BEFORE you go killing off their Ivy.
Ask if they keep it for the wild bird life and take it from there because they'll be furious if you kill off what they want to keep.

I would have thought that any strong strength weedkiller would do the job though, contact a gardener and see if he would supply you - or carry out the work for you ..... the commercial strengths won't be available to the public.