Short-term accommodation for travellers is indeed available. If you want to sign a short-term rent contract, then you should start your search on rent listings site in the UK such as SpareRooms. We had this situation once at a company I worked, where they hired a summer intern for two months. He was able to find a short term rent contract within a week. However, short term contracts are usually easier to find in summer months because that's when landlords typically have rooms free for a couple of months which may usually get rented out to students (say). I don't know how easy it will be for you in January / February.
Alternatively, and this is possibly a more expensive option, you can also check Airbnb.