As L O'L states, every university faculty is free to determine its own admissions criteria.
However, most faculties would probably consider results with the same UCAS score as their offer to be acceptable. The obvious exception would be if the 'C' grade was in a subject which formed a core part of the syllabus to be studied at Uni. e.g. if you were hoping to study a subject which involved a great deal of advanced mathematics (which includes many of the sciences), getting a C for your A-level Maths might exclude you from the course.
Chris