This is going to be course and university dependent. Even at a single university (presumably Durham as you posted it in this forum) it will probably be variable depending on your course what exact dates there are.
That said usually in the UK first term exams happen in January before the second teaching term commences. But you should absolutely discuss this with your personal tutor to see if there are expected to be any outside of a given "January exam session" and if not, when said session is.