You sound like a really good neighbour. If the hedge can be cut back still, why not go with that? You wrote there is a fence underneath all that. Must be sturdy, or on the cusp perhaps?
As an update, the (friendly) neighbours hacked the hedge-fence back hard this year. I asked them not to go in too hard as the hedge-fence would collapse as the thick branches of the (30 year old) ivy is holding it up. But they cut it right back and, hey presto, the hedge-fence is collapsing. So
a) we lose the green wall - wildlife haven
b) I have to replace the fence and pay for it myself
I am a bit narked as they did what I specifically asked them not to do - explaining the very likely consequences. They had agreed.
Both sides have to maintain a hedge on a boundary. This has proved to be a difficult issue. I'm irritated that their actions means I now have to shell out hundreds and that this was avoidable and they had previously agreed that it was not a desirable outcome.
I wouldn't overthink it. Just carry on as you are if it's what you want. I don't imagine it's doing the fence any good though. What about a hard cut to the ground, reset the whole plant and get it growing fresh again.
@Fire, just ask them if they'll go halves on a new fence. If not, you are not obliged to have a fence on a boundary, you could just plant a new hedge, using cheap native hedge whips. It's not quite correct to say both sides have to maintain a hedge, unless it is a shared boundary. The person who planted the hedge should take responsibility for maintenance both sides. In practice, because it's easier, both neighbours usually do their side, but it's not compulsory.
I'm with @Lizzie27 here, if your neighbours want " a fence" let them take it up with their landlord. If you want a hedge, then plant one on your side of the boundary .
I think I need a photo. Is the fence that's falling over designed to mark the boundary between your gardens or be a security screen too?
If the former, just a couple of posts and wires will do the trick cheaply and effectively and you can then plant your own hedging plants on your side, choosing the plants according to your taste and needs for wildlife, colour, security.
If the latter, make your new hedge very prickly by combining pryacantha and hawthorn - both cheap as whips or young plants - and let any surviving ivy scramble thru it.
Vendée - 20kms from Atlantic coast.
"The price good men (and women) pay for indifference to public affairs is to be ruled by evil men (and women)."
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If you, the neighbours and their landlord are OK with the current arrangement, I'd leave it at that.
The landlord is probably happy as long as the ivy doesn't get onto his house and the maintenance doesn't cost him anything.
😠
If you want a hedge, then plant one on your side of the boundary .
If the former, just a couple of posts and wires will do the trick cheaply and effectively and you can then plant your own hedging plants on your side, choosing the plants according to your taste and needs for wildlife, colour, security.
If the latter, make your new hedge very prickly by combining pryacantha and hawthorn - both cheap as whips or young plants - and let any surviving ivy scramble thru it.