I can never understand this, letting dogs bark all night. I mean, either your neighbours possibly work shifts and aren't always home, or they're out every night. Otherwise, how can the dog owners put up with it themselves?!
We had new neighbours who left their dog outside in a little kennel during the day when they went to work. He yapped constantly from the minute they left, until they returned. Several of our neighbours moaned about it amongst themselves, but I was the one who decided to put a very polite note through their letterbox. I simply said that they were probably unaware, but I thought they should know that their little dog was constantly barking, and he possibly had separation anxiety when he was left alone. I kindly asked if it was possible for them to keep him inside, so as not to disturb the neighbours. Straight away, they kept him in the house, and arranged for a dog walker to take him out daily.
I know that your case is slightly different, Beswitched, with it being a night, but perhaps a polite note may help, if they are reasonable people ...