Healthcare professional with some experience in mental health and emergency medicine here: This is the way to go . Your problem is NOT the noise. The noise is a nuisance but not dangerous. The fixation on your brother is. Because there is a high risk here,that once “noise” doesn’t cut it from the point of view of the patient, he will resolve to other means.

As said before:

• Document everything, make a detailed protocol about everything he does or says towards you.

• Call the police, especially when he threatens you or your brother or claims he is intruding. Make sure that every member of your household is as polite as possible to the officers. If they refuse to do something accept this but kindly ask for their names or collar numbers and the name of their chief constable. Then write a very polite letter to the CC making it clear that you understand the difficulties the officers face but how you feel threatened and miserable and ask for help and advice to resolve this. (Why being polite? Because then it is nearly impossible for any copper to frame this as a *neighbours dispute" or anything - and coppers in the UK are far more inclined to help “members of the public” they see as pure victims themselves)

• Depending on where in the UK you live contact your “Single Point of Access” mental health team. They are, well, the single point of access for mental health and by definition also are the contact points for friends,family,etc. of mental health patients.There is a good chance of them already knowing him, so that might help. Also,if your mom gets sicker from the whole ordeal, call her an ambulance - more freely than normal, to get that on the file. (And yes,I know this is a moral grey zone)

• Call your council both in terms of mental health and nuisance laws. Be nice,but pressure them to do something.

• Find out who the landlord of the neighbour is (if he doesn’t own) and contact him as well as your own landlord.

Again,let me repeat: The noise is not your problem. The noise is just a symptom of your problem and when the noise goes away and the problem is not resolved something else will come up - very likely something worse.