My back garden backs onto another garden, and when I moved in the people living there at the time had a bull mastiff (lovely dog) that they never cleared up after.
The smell was unbelievable, especially in the summer. It meant that neither myself nor any of the neighbours could bear to sit in our gardens. My bathroom and bedroom windows had to stay closed during the summer as you could smell it from 30 feet away. The people immediately neighbouring the house with the dog couldn't bear to open their windows ever, even in the winter (we live in terraces so it's all very close together.)
Eventually we all called the Environmental Health Officers round. The guys took one look at it and were disgusted. After three official warnings with not much result (they would clear it for a while, then it would deteriorate again) the EHOs put a prosecution case together. Altogether, eight people living in the street had complained about the smell.
The dog owners were taken to court and fined. After that they got their arses in gear and things improved massively. Shame it had to get to that stage, but there you go.
They moved out about a year ago. The people that live there now have two dogs, and two cats as well. The yard is spotless.
Do call the EHOs in, OP. This is a health hazard and impacting on you, therefore they must take action.