[rwmj]

Oxford & Cambridge are very selective and entry is very competitive. Unusually for UK universities they hold a separate entrance exam for all courses. (Information about the extra admissions tests done by some universities and some courses: https://www.ucas.com/applying/before-you-apply/what-and-wher....)

Fun fact: When I applied to Cambridge I was interviewed by Mary Beard.

[nephihaha]

Entry is to Oxford and Cambridge is by interview. A lot hinges on that.

[jvvw]

In maths, if you do well enough in the exam, you have to really mess up the interview to not get in though I would say. If you're borderline, the interview is important though - the interviews will usually be 95% maths questions so it's more like doing an oral exam where you have to explain your thinking process and answers.

[nephihaha]

I'm sure it probably depends on the discipline (and indeed the college, since some are harder to get into than others). I can see how this would be important in mathematics where it is hard to avoid rules and structure. In other areas, the decisions will be much more subjective.