What would be your best advice for someone going to interview at Oxford or Cambridge?

First of all, be happy with yourself that you've got this far! If they want to take the time to interview you, it means that you've impressed them and they want to get to know what you're like as a person and how you think! For this reason, I think it's so important to go in with the mindset that this is almost a mock supervision / tutorial. You want to find out as much as you can about whatever subject you're going into! You should be enthused by what you're discussing and you need to show that! Speak out loud. For example, I was asked to think through a chemical reaction mechanism which I hadn't encountered at A level, so I made sure to explain, I haven't seen this before, however from the reaction mechanisms I know already, I know these are the principles of why a species may attack another. Thinking about the reactants, I know they have an electronegative atom here etc. They want to know what your thought process is, so make it easy for them! They'll help you if you get stuck and although the majority of people think their interviews went badly, the people who did are often the ones who get an offer! Good luck, but it's really not as daunting as they make out!