None at all, il Plod will, at a local level, have no idea what to do with it at all, and most likely unless someone’s been murdered, just park it in the in-tray marked ‘bin’.
Unless you can prove anything crime has been commited, and that you have evidence to that effect, then expect no response at a local level.
At a national level, you will expect the police high tech e-crime department to take it on, by requesting logs from the ISP in question, once they can prove irrefutably that the postings or harassment came from it, and not hidden behind a proxy.
Because of proxying, you’re chances are next to nil.
I would rather look at a social element of the haressment and see if evidence is given away along the lines of ‘I did this, at this time, from here’ most usually by way of a tweet, post on a forum or a picture.
Anything else is just subjective heresay.
Trust me on this.