Can neighbour paint their side of brick wall if wall is on our side of garden?

You seem to be saying that the wall would be on the boundary between you and them. If this is the case then they can paint their side so long as it does not cause damage to the wall. If you build a wall on your property you may affect the deeds to your property which could lead to problems if you ever get to have boundary disputes or when you sell your property. You do own what is on your boundary for the most part, certainly fences and walls, but if you share a boundary your deeds will state whether it is shared or you own one fence or the other. In Leicestershire for example most properties own the fence/wall on the right hand side as you look at the property from the front. In other places it is the left, in some it is shared. So check your deeds first. My only thought is, if you can't see their side of the wall and they are not damaging it, why worry if the paint it?

Would love help but your question dosn't make sense peter