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Thanks for the suggestions. I will speak to them next door, and will also speak to the CAB and check our deeds etc.
When we viewed the house we could hear the chickens and the noise wasn't a problem at all - in fact I quite liked it, I thought it was a nice change to hear them. However they have grown in quantity since then, and I don't know if it's because it's summer that they smell worse - (we bought the house in Nov!) or if they're not being cleaned out enough.
Our other neighbours can smell them too and the noise bothers them but they haven't mentioned it to them.
I am consious that we moved in after them and their animals were there first - and don't wan't to fall out with them, but can't see that it's healthy to have that much poo rotting in a garden. My other neighbour said he saw a rat last summer and he's lived in his house for 35 years, and had never seen one before - and if I saw one that is one thing that would tip me over the edge. I would have no hesitation at all in going to the EH if the poo starts attracting attention like that.