When you own your own home, it will be very obvious as to whose responsibility it is to deal with such problems such as rats and mice. However, when the property is rented, it is far less clear who should take the time and effort to resolve such a problem.
There are two parts to this, and not only is the legal responsibility of the issue often a grey area, but it may also fall down to proving whose faulty an infestation was, something which can be very hard to get to the bottom of. In fact, it may come down to proving whether or not the infestation was there prior to tenancy or not, and the chances are no one involved will actually really know.
It is often best for tenants to simply deal with such problems themselves. There are many reasons for this, but not only could waiting for landlords to sort the problem lead to discussions of culpability and blame which will take a long time to resolve, but should landlords be busy, the problem could get far worse whilst you are waiting for them to rid your house of said pests or whilst you are waiting to see if they will take responsibility for the infestation.
Mouse traps are fairly cheap to buy and easy to use and therefore those with such pest problems are likely to find a much easier, cheaper and quicker resolution to a pest infestation by simply buying such products online. There will be all manner of different ways to get rid of such pests, and some will be far more humane than others, and simply looking at the available traps and mouse poison will help you see which will be the most effective and the most suitable for your own particular needs.
So, whilst the question of culpability may well be a grey area and something that takes a long time to resolve, the actual problem of pest infestation can be resolved fairly quickly by tenants simply being proactive.