Oh dear god. Just when I'd forgotten about my previous rat problem, I read this and it all comes flooding back.
Right. Don't bother calling out the council. They will do nothing that you can't do yourself.
I had one just after Christmas and it took me nearly two months to get rid of it... kind of. People thought I was being dramatic, but it literally took over my life and was really stressful.
I put down traps, loaded with peanut butter and snickers bars (someone on here told me to use this) but no bites whatsoever.
I then put down glue boards (minging but I was absolutely desperate) but these didn't work either.
I then decided to go down the poison option, which I didn't want to do because the ratman from the council told me he could eat the poison and then die behind the kitchen cupboards/in the wall and I wouldn't be able to locate the body, and every night topped up the bait (it was pre-loaded with the poison).
I came down every morning to find some more had been taken, but just kept going with it for about three days when nothing more was being taken.
So, that was that and I just assumed ratty had crept off somewhere and died. Little did I know that he had, and he was now about to rot under the floorboards!
I kid you not, it was the most horrific thing I have ever EVER smelt. I tried absolutely everything to find him, but never did.
I got my friends dog in, I borrowed a cat, bought a deoderiser from Rentokil, had most of the downstairs floorboards up, nothing got rid of the smell or helped me locate the bloody thing.
All in all, it took over a month to kill the damn thing and then a good two months for the smell to go - which only happens when the body is fully decomposed. I can't begin to tell you how horrendous the smell is, but I would walk through the door and start heaving. I wouldn't have anyone visit my house, windows were constantly open and the central heating was constantly on - which made the smell even worse but rots the body quicker.
You have my sincere sympathy because, if it ever happened again, I would just pack my suitcase and set up camp at my parents!
Go with the poison, it's much quicker than faffing around with traps, but I hope for your sake it goes outside and finds somewhere to die.
Ratter gave me loads of really good advice, so he's your man :-)