I'll echo the comments from the others, talk to the neighbour first, see what their objection(s) are. It might be something simple that can be overcome easily, or it might be like many folk today, they've become very disconnected to nature, a sad sign of the times.
If all else fails, then definitely talk to the council Environmental Services dept, they usually handle noise concerns.
If you feel that is going nowhere, contact the RSPB direct, local Wildlife Trust and a few others may be able to give guidance.