...the bottom of a 50m garden? We live in a residential/rural area in Sheffield. He is complaining about the noise, but we are closer to them and we don't notice the noise from the house. He says he's going to take it further.... what can he do?

I love ducks! Sorry that you have neighbors who don't. I don't know your local laws.

If its a residential area (high density urban area) there are council bylaws that control the keeping of fowl.

It is prohibited in most designated urban areas in the UK .
No problem in other rural areas generally. Your best bet is to check out the local bylaws with the Local Authority. They will able to advise if these apply to your area.

If the laws dont apply, keep your ducks well fenced and ignore the eejit.

I keep 6 Kaaki Campels on a 1/3 of an acre and they are quieter than the neighbors, their dogs and their floodlights (aargh).

Best of luck

depending on your local zoning (usage) laws and the noise ordinances he quite possibly can.. is it possible to reach a compromise with him? You could also ask your local animal authorities what your rights are.