there are laws regarding keeping such in other countries. As far as im aware there is no National Law about keeping chickens or cockerels in a residential area, unless it is a commercial enterprise.
However, there may be local bye-laws about keeping livestock, or there may be restrictive covenants on your house or land which govern the keeping of livestock. There is also the laws relating to "Nuisance" - whether from noise or other. have you been to consult Citizens advice?
Just a thought, have you tried housing the cockeral in at night and release in the morning? A well built block shed or such, or good dark sound proof area? just to show compromise.
I would start planting tall trees to obsure view and act as sound barrier.. i planted 15 laylandii 3 years ago and mulched with some lovely rabbit manure.. they have grown a serious amount and have covered a great area - excellent result ( i know there are restrictions on these trees- i was very sneaky and planted on the railway embankment
) )
I have the same problem with my next door neighbour ( the curtain twitcher) no matter what i do she is there watching and glaring. This week we had environmental health around checking, but they went away more than satisfied that everything was A1. she had a flea in her ear. she had complained that the stock was causing too many flies... but after investigation it was found it was caused but the food she throws out and that my yard and stock were more than over clean......
2 years ago she complained constantly that i should not have painted my house with dulux weather sheild 'white' as it was too bright and she didnt like the colour
.. my trees are to wavey in the wind? My decked area of the garden was too large! My kids bounce their basket balls in the day time!!! the list goes on. Ive had ten years of this! I can empethise fully with your plight.
Fortunately for my sanity my house is near completion and will sell as soon as i can.