Nope. If it is not for commercial use, then you can legally keep a cockerel at a residential address (There may be local bylaws that date back go knows how many years regarding the keeping of livestock which prevent the keeping of a cockerel, but this is not a national law).
People can still complain if the cockerel makes lost of noise at inopportune times, but it's just like any complaint about unsociable noise, not because it is a cockerel.