@philippasmith2 and @wild edges Good points re the guttering and roof overhanging. I had always assumed that the garage wall was the boundary. Never thought about the overhang. I have all the registry plans / transfer plans for the property so I will check. Boundaries are so hard to define though even with the plans.
If you think that's bad my friends NDN drilled her house walls and hung his ladders off brackets. He was really offended when she told him to take them down. Some people are unbelievable.
@Chocgeorgie, if your guttering were damaged by the neighbour's plant, I wonder if your house insurance would pay out, or would they decline a claim on the grounds that you knew about the plant and did nothing? Suppose you were to write to your insurers, telling them what you've told us, and giving the neighbours a copy of your letter, with a friendly covering note, and of course, keeping a copy yourself. Then maybe the insurers would write to the neighbours and spell out the legal position. That might make them take notice.
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It's astonishing how people behave, and can't seem to understand why folk get p*ssed off.
I live in west central Scotland - not where that photo is...