nuisance phone calls come under the Malicious communications act, is also regarded as a form of harassment in extreme cases.
A crime report can be made under the malicious communications offence.
Police have training under the RIPA act, basically when speaking with the mobile phone operator and gaining details about the caller, justification has to be made that no intrusion of the callers human rights are being carried out, and that the request for caller information is wholly justified to prevent or detect crime.
Once the subject is found out, they can be warned by police against their calls/words over the phone, and advised not to repeat their conduct otherwise repeating the offence after a WARNING to CEASE would amount as Harassment and to commit a second offence, being a course of conduct complete knowing what they are doing is causing harassment/alarm/distress to the recipient, makes them liable to be arrested. This info from phone companies to police has been known to take up to half a year to get.
That is the criminal line of enquiries, but ther will be civil routes that you are obvoiusly looking at.