There's a rat in my kitchen - what do I do?

So... there appears to be a rat in my kitchen.

I'm renting a terraced house. One of the adjoining houses has a couple of dogs, a back yard full of dog**** and bags of rubbish. There was a lot of activity in the house next door this morning, whether the tenants decided to do a spring clean or whether they've gone and the landlord has embarked upon the unenviable quest of cleaning up after them. I suspect they disturbed the rat and that that's why it's ended up in my house - though I'm not long back after Christmas, so I suppose it's possible that they were here before.

The house is oddly built - the kitchen is more like an almost detached pantry stuck on the back as an afterthought. It doesn't appear to be terribly well finished behind the presses and the cooker etc. from what I can tell, and I presume it's shoddily connected to the kitchen of the house next door. The door from the kitchen to the rest of the house is closed at all times, so hopefully they won't be able to get in any further.

The previous tenant informed me that they had rats during the summer and that they had the exterminator in. I had assumed it was due to a combination of the heat and the mess next door, though I suppose this is not necessarily the case.


TL;DR - there's a rat in my kitchen.

What should I do?

I have no qualms about the rat(s) dying, though I don't want their rotting corpses to stink up the place.

I saved a spider from the bath this evening - I feel karma has let me down here.

I'm going to just bin all the food I have in the kitchen now (not much in it anyway - a perk of living alone) so that there's nothing to draw them back. It can't be the warmth they're coming for - it's a whopping ten degrees in here now and the kitchen's even colder. Suppose I should hoover the floor for crumbs too.... sigh...