Make sure you get a hold of a complete copy of the by-laws and perhaps have your landlord read and sign a copy to show the complaintant. There should be no need for proof of your enclosures unless the complaintant contacts the police and they ask to see your enclosures. If everything is set up in adequate cages and you have nothing to hide, I would allow the police to view your collection just to make the point that all is well and quite normal
Have the by-law available for them too. Other than that, there isn't much to do.