I don't know about the legal tenancy issues or who is responsible for getting rid of the rodent but frankly in your situation I'd get rid of it first then ask questions later. We had a nest of rats in our garage a couple of winters ago and got rid of them for the grand total of £5, a box of rat poison from Wilkinsons is all it took, laid it in the garage, they ate most of it and we never saw the bodies but they didn't come back (and they'd been in the garage over winter).

You can't stop them, they are scavengers and everyone throws waste food in their bins so if you leave the lid even slightly open its feast time for them, if they constantly feed there then they will find there way into your house - best to shut down their access to food outside and let them look in your neighbours house instead.

My concern was if they die they will leave a awful smell decomposing away under the kitchen sink maybe. Issue with bin is the council still have not provided me one ringing them again Tuesday. haveing to use a old style bin with no lids. Going to get a tub off the stuff from wilkos though and lay near the bin.

Rat in the kitchen?

Call these lot, they'll fix that rat.

As far as smell goes, you will never smell anything like it if they take up residence, forget what people tell you who keep them as pets, they defecate anywhere and everywhere and in large quantities and it smells really bad, when we got rid of the ones in our garage we had to strip the place empty, throw away anything that they'd been near and give it three scrub outs with disinfectant before the smell went, you really don't want them in the house at all.

You are a private resident, so it's down to you, probably on an AST agreement which means it isn't down to the landlord or agent. Call the Council and they *may* offer to send pest control, but that is going to be £40 minimum, renting doesn't abdicate responsibility.