You don't need a paper contract for one to exist, it can be formed by action. If you've been paying the rent on a monthly basis for some time (by bank transfer? i.e. can you prove it?) then that's probably enough to form a tenancy contract. As everyone else has said, you should be given two months notice, and depending on when this tenancy began, there is a process to follow (post-2015 tenancies, a specific form you must be served with), and then of course failure to leave means the landlord has to go to court to get you evicted which takes ages, months at the very least. The trouble with all this is it relies on them actually following due process.