Conifer dying from Ivy

[Chef_uk]

I've had to cut out some dead branches from our 8ft conifers. The ivy on the neighbours side is bad and that's what is killing the trees. I probably have two that are untouched with good growth on them. Should i cut down the other 3 trees so i can get right in there to clear out as much of the Ivy as possible?

[TEB]

But Ivy isn't parasitic, unless there are huge amounts of it and blocking out light