re "strangling trees" - ivy gets a bad press - yes there can be too much of it on a tree so it weighs it down but it doesn't actually strangle.
It's a great wildlife resource - birds nesting, hiding from predators, likewise butterflies, solitary bees etc overwinter and in autumn there are hundreds of bees and hoverflies taking nectar from our ivy hedge, right now the blackbirds are eating the berries.
It's a great plant - but two places you don't want too much of it - with very crumbly mortar and letting it get too high up walls and under slates etc -- easy answer - trim it, you don't need to eliminate it.