I know of someone very very stubborn who had kept chickens and cockerels on some land for 40 years (not the same chickens obviously
)
A newby to the villiage took offense at the noise of the cockerel and complained to the council, and complained and complained and complained.
The council had to investigate, which they did and of course it was found to be a noise nusience because of the early morning crowing and nothing else. The owner was told by the council firstly to shut the cockerel up and stop it crowing early in the morning
he couldnt keep it quiet so eventually was told to get rid of the cockerel.
He wouldnt get rid of the cockerel (like i said, very very stubborn). He had several threatening letters from the council because he hadnt done what they had asked him to do. The council (like most) dragged their feet and didnt really really want to take things any further but had to act on the complaint.
Five years this went on and very very stubborn man even bought more cockerels in (i'm sure just to antagonise the situation).
He said he would rather go to prison than get rid of his cockerels and i do believe he meant it.
Back to your problem. Like most have said yours probably wouldnt make enough noise and im sure if the council did investigate they would come to the same conclusion and in extreme circumstances would set up noise mointering equipment (though i would find it unlikely to happen) as mum' mentioned they will also be interested in any smells, what you do with the waste, any potential rodent problems etc.
Before i got my chickens, i rang our council and they were very helpful. Maybe you could ring yours and find out what is acceptable and what isnt and let them know about the problem neighbours. Even invite the council around (then stick a note through nasty neighbours door and tell them you've beat them to it)
Some people like to make a problem where there isnt one and spread misery wherever they are.