Remember that the interview and hence getting into the course is just step one - you then need to actually do well on the course! Degree level maths is vastly different to A-level Maths, so I'd definitely recommend if you're interested in a maths degree you look at some content which is representative of degree level maths. Any kind of introductory analysis textbook or similar would be suitable, as would potentially be an (abstract) linear algebra book or something on number theory or foundations.
The chapter zero of Munkres' A First Course in Topology I think covers a lot of stuff which is indicative of degree level maths study and should be reasonably accessible from first principles I think (the rest of it not so much probably). Spivak's Calculus is written specifically to be accessible to both high school and degree level students. There are also lots of "bridging the gap" type books applying and presenting A-level Maths topics (e.g. matrices) in a more rigorous way like Earl's Towards Higher Mathematics.
In terms of preparing for the interview (and the MAT), doing MAT practice papers would likely be helpful. For the interview more specifically looking at some STEP preparation resources may be useful. Likewise UKMT prep resources might provide some relevant practice. Also generally thinking about what you have studied and a) how/if you can generalise it and b) how you can apply it to unusual/unfamiliar problems. Note I don't think any of those are necessarily that similar to degree level maths in of themselves though...