We have prob with rats as we back on to woodland which is not cleared by the owner. so there are years of over grown brambles which have died back and gown again. Grat rat breeding ground. We clear it about 20ft back from our fence, but they still come down.
I never ring our council as they never really solve the problem enough and I have to pay £25 for the visit. So for £25 a visit I decided bait & traps. I use eradirat and some "advanced" rat trap catchers from b&q. I have a humane trap, but it isn't very effective. In 4 years we've only ever caught 3 rats in it. The traps are not for the squeamish as they kill the rat instantly by breaking it's neck. They are on a hair trigger and really hurt if you get your thumb stuck in it. I have them attached to a chain which is attached to the ground, so they can't take the trap away. I also use a long piece of old large drain pipe secured down to put my bait and traps in. this is because we have two dogs & a small child who'd eat the bait from the trays and the traps given the chance. We've also got purpose made metal bait stations which is locked and secured down next to our rabbit hutch and chicken pen. Our feed is in secure proper feed bins too which helps. All our garage/shed/outbuildings are rat free as on a high shelf in each I leave a small amount of bleach in open topped bottles as they don't like the smell.
We occasionally find the Rats in the traps - stone dead and we rarely see a dead one from poision as apparently they go back to the nest to die.
I think the key is to put what ever method in the line of where they run and be consistent at rebaiting and checking them. Dh does ours daily whhilst he has a ciggy in the garden. The rats in our garden run down the hedge and between the flower pots. We used to have a wooden shed which was raised off the floor which was perfect rat hiding ground. the shed was torn down as we didn't need it anymore and the floor had been eaten and was rotting away. We have a small bit of decking (4ft by 8ft) which has a trap and bait under, but they've never touched it because there is no food in the vicinity.
We've also stopped feeding the wild birds - 2 reasons the birds would knock the food over the floor and 2nd avian flu when we got the chickens was a concern and didn't want to increase the risk. This has helped not encourage them.
this is my experience and you might not agree with the killing of the rats, but I don't like them and what disease they bring with them, so they die I am afraid.