Paint my neighbours fence?

[sierra2020]

Both my neighbours have the wooden fence up which separates our gardens, we are getting our garden done, and my builder is saying I don't need to put a fence up, seen as my neighbours already have the fences up. As one is only needed to separate the gardens. He said I could paint my side of the fence.
Can I actually do this? I know it's my side, but isn't that the property of my neighbour?

It's a old house. The wall has cracks everywhere, no longer straight. It looks hideous. We won't be taking any of their boundary. The wall is ours and there's a clear line that separates our houses.

@VeganCow spray painting their fence did cost our neighbours close to £5000. They managed to coat our garden furniture, 2 bikes, artificial grass, awning and paving.
Grass, furniture and awning needed replacement, paving and bikes could be (kind of) cleaned (its still visible). it was a hot day, and we only realised the day after.

If you are removing a wall and it exposes the fence that's entirely on their land you would be gaining 9" minimum of garden though? (Based on average thickness of walls).

If it's an old house I'd be trying to repair the wall, much nicer than a fence imo.

I'm another one whose neighbour decided to use a sprayer, on a slightly breezy day 😏
Our back door and side windows were covered with brown spots, as was our patio, and my car!

Well quite frankly it's not my issue if I gain 9" of their garden(I won't like I said) but if I did, am not complaining, why would it be my concern if I did gain some of their garden, if neighbours are bothered they can rectify their fence. But I otherwise will have slightly larger garden without the horrible walls.

‘My neighbour has painted my fence it’s all drippy on my side and looks a mess, he’s also painted the top so my side looks awful. Ask before you paint!’

This.