Talk to your council and get them to explain what it means. I’d guess the concern for them would have to do with rainwater running onto your neighbor’s property but they might have something else in mind. If you talk to them at least you know what you are dealing with.
Many people have open top runs. I have a large area surrounded with electric netting and hawks all over the place but have never lost a chicken to a hawk. Many people have though, it is a risk. Climbing predators will be a risk on your open top run too, but still the run is a deterrent to many predators. No one can give you any guarantees on any of this but you might be quite successful with an open top run. I’d certainly lock them in a safe coop at night.
The other issue is that the chickens might get out. Many people would be shocked at how high a full-sized chicken can fly if they really want to. Many people keep chickens contained in a relatively low fence. The key is motivation. Some chickens are pretty easy to contain, others really like to roam. It’s hard to predict what a living animal will do. They are all different.
Mine stay within that 4 feet (1.3 meter) high electric netting without much problem, but that is a huge area. When one does get out it is usually because there was a pecking order/dominance issue with young cockerels or a hen was trying to escape an amorous rooster. They get trapped against the fence and go vertical trying to escape. Sometimes they come down on the wrong side of that netting. If I were you I’d build it about two meters high and hope for the best if it is open topped. If it has a top you need to be able to walk in there without banging your head anyway. That hurts.
Something else to avoid is a solid top to the fence. Chickens really like to perch. If you have something on the top of your fence that looks like a good place to perch, they are very likely to fly up there just for the joy of perching. They might decide to hop down on either side of that perch. If you leave wire sticking up a few centimeters above your top fencing horizontal support they are a lot less likely to fly up there.
I suspect if you chat with your council you will get a good answer on this. Sure hope so. Otherwise, good luck.
