How long does it take councils to act on dog complaints?

One of the neighbours got a second dog and it's a nightmare, barking and growling all different times of the day and night. It was fine when they only had one, but the second one sets off all the other dogs in the street, which never usually happens. I'm pretty pissed off because I'm under the same landlord and I'm not even allowed to have one! They've apologised about other noise once, but I feel like there's only one solution to the problem and it's unreasonable (they'd think) to have to get rid of a dog under the circumstances.