To be fair though at this stage community police wouldn't get involved unless neighbour was making a real nuisance of herself harassing neighbours
So a few letters to various neighbours asking bizarre things such as 'don't put washing out on your line it ruins my view', 'close your windows when cooking as the smell makes me nauseous', 'oil your squeaky door, it irritates me', 'stop whistling as I don't like it' etc... won't trigger a response.
But if she comes 'banging' on your door repeatedly (or anyone else's) to complain about innocuous (bizarre) things and you'd asked her not to, and if she sends multiple letters and you'd asked her not to, then that forms part of a pattern as it is unreasonable and starts to become harassing.
Helpful if she is showing same pattern to others, then maybe community police officer might have something to chat to her about.
My feeling is if she continues being Ms Complainey Complainerson, get in touch initially with landlord to advise she is starting to cause nuisance to neighbours.
Obviously if she threatens you or behaves in aggressive way, that's different as that may be reportable offence or indicate more serious issues.
At the moment she seems an intolerant neighbour, who is a bit strange or entitled in what she feels she can dictate to other people. I wouldn't be suspecting actual diagnosable MH or LD problems from this info. The criteria to diagnose is set far higher (than info suggests about how this lady functions in general, unless she seeks support herself via GP)