the ico
https://ico.org.uk/ covers the law on privacy and this includes cctv systems.
Unfortunately they rarely will give you any direction on if a situation is allowed or not.
If you need to film a public space you need a legitimate reason and need to register the cameras with the ico, this is constantly changing.
You do not need agreement of your neighbour to film a shared area, you need to have good reason.
Your neighbour may not agree if they are the ones causing the damage.
You should review whether you still need to cover a certain area on a regular basis.
My opinion, if damage is occurring without cameras in place, having them is reasonable to find out the cause/ stop the damage from occurring.
If you found it was a person doing the damage and having a camera stops the damage from occurring then the use of the camera is justifiable
If the damage is done by a wild animal, then having a camera won't stop the damage from occurring? and therefore questionable if actually needed.
You cant film from your property into your neighbours property, even if you suspect they are planning to kill you(not likely), but I would suspect anyone going to do that to a neighbour would make sure you couldn't see or hear them anyway???
You could use your privacy filters or have an agreement with your neighbour to cover their property, but you would probably need to outline why this is being done, should your neighbour fall out with you or move then you would probably need to review your agreement.
Audio, the concern is eaves dropping, but say a neighbour has been verbally threatening you, it wouldn't be unreasonable to gather evidence which is what the police would ask for, and recording of audio like the CCTV images themselves aren't going to be looked at unless there was some kind of incident and wouldn't be kept.
I have customers with shared access straight through their gardens, damage was occurring cameras went up and it stopped, completely justified.
Have customers filming the road leading up to there house, reason they have had several vehicles crash into the wall and damage it and then they leave the scene and someone has to have their wall rebuilt.
one particular case the customer is looking at traffic coming from a certain direction as it is from this direction that those crashing into the wall come from.
It hasn't stopped people crashing into the wall unfortunately, but it has stopped them from fleeing the scene without leaving their details. saved them a small fortune in repair costs.
Looking at the footage it can be seen that the vehicles are travelling too fast and lose control, especially in cold weather.