I think your advice is very sound. However, just a word of warning as I’ve had a slightly different experience – making a complaint to the authorities instead of contacting the neighbour directly as they did seem utterly unapproachable. Trouble is the neighbour called me on it, I admitted that I had done this and they then blew their top that I’d gone straight to the authorities instead of speaking directly to them and was very threatening. A very unpleasant experience indeed.