I have had complaints about my dogs from a neighbour, and the council wrote to inform me. I contacted the council who said if they got any more complains they would instal monitoring equipment. This happened and they wrote to say that the barking was not at unsocial hours or for any length of time so they would not be taking any action. However the neighbour still complained and once againt the monitoring equipment showed no prolonged barking.
The lady from the council said they would still take no action but to try to reduce the things that made them bark, such as putting a postbox out the front so the postman didn't have to touch the letter box, covering any doors/windows so they could not see cats or bird on the fence, leaving them in a room or part of the house where they could not be heard so much by the neighbour.
This seems to have helped, but the lady from the council did say that if they still got complaints they would have to investigate again and if it was proved to be a nuisance they would have to issue an abatement notice, and if I did not comply with this they would then go to court.
Hopefully this will not be necessary, but it does show that they investigate fully before doing anything, and it is a fairly long process.
There is another dog near me who is left out and barks almost constantly, not parcticularly loud but that one tone monotonous woof, woof, woof of a lonely and bored dog.
It does get on my nerves but I realise that it is not the dog's fault, and would not like the people to maybe take it out on the dog if they were reported.
Definitely contact the person at the council, and ask if they can tell you when they are saying the dog is barking, and ask for their advice - this gets them on side and if you can get a few digs in about the neighbour so much the better, provided you are clever about it! Good luck, I know how upsetting this can be.