1. There are two aspects to this issue. The first arises from the law of nuisance. The second would arise from the European Noise Directive. For the purposes of the answer, I assume that this person complaining is not one of the two immediate neighbours within 50 metres of the property but is from the huddle of houses about 200 metres away.
2. Under the common law of nuisance, the standard applied is reasonable user of property within the locale in question. Here this is a rural area, 3 or 4 mile from the nearest town and the primary activity is agricultural. So agricultural activity is an accepted part of the neighbourly give and take in the law of nuisance. Having cockerels in an agricultural area is not an unreasonable user of land. This man would have to show that the noise from the cockerels was persistent and exceeded 45 Decibels in sound level on a persistent basis for him to have a case in nuisance. Given that the nearest neighbours don't have a difficulty, I very much doubt that the noise levels constitute a nuisance here. One expects animals such as cockerels in a rural agricultural area. it is a normal part of rural life.
3. Under the European Noise Directive, this man would have to show to your local Council that the noise levels were excessive and once again exceeded 45 Decibels where he is living and on a persistent basis. If the noise of the cockerels don't exceed 30 decibels, then they can be as persistent as they like and no remedy will be granted by the Council. Be aware here that it is your local Council who would have enforcement powers here. This man cannot seek enforcement himself. The threshold of human hearing is 0 decibels. 50 decibels is normal conversation beside you. So that gives you an idea of what is involved.
4. Finally, I would advise you to investigate further. Be aware that it is your tenant who would owe this man a duty under the law of nuisance, not you. Additionally, if the Council was taking enforcement action, it would also be against your tenant, not you.