Twee
What I think you should do is make a point of how neighbours should behave.
Speak to your neighbour to tell them you are painting your side of the fence in blue and ask it is ok to come around to wipe away any excess drips over to their side. And then as a casual remark, mention that the last time, they sprayed their fence brown, overspray had gone on to your conservatory. A bit of co-operation between neighbours might be handy to stop this accidental damage occuring again.
I own a boundary fence with a neighbour and was very careful with spraying using a brush to areas where overspray might affect the neighbour property. I also used a similar colour so any drip through would not look unsightly. I have found that if you can have ok relations with neighbours it makes life easier. My fence was blown down and my neighbour helped put it back up, picking up some materials for me, which I paid for.
Brewerdave1
You only have a general duty of care to maintain the fence, so that it does not endanger your neighbour in anyway. How unsightly a fence may be, is down to person preference. A few bits missing, may add a 'shabby chic' style to the garden. If I were you, I would just repair the fence and if they say anything, just say sorry this is all that I could afford.
Huckster