As far as I know, if the caller becomes a 'pest', then you can get the calls logged and traced, it takes a while, but it can be done.
Of course, this only provides the details of the person the phone was originally registered to. For example, I could lose my phone tomorrow, somebody could find it and commence making nuisance calls (although I could block the phone based on the IMEI).
However, in most cases the numbers are registered to the actual owner.
You really need to contact your provider, be it BT, or mobile...