What can I do to impress Oxbridge interviewers and what are they looking for?

Oxbridge interviewers want to see how you think. One tip is to think out loud, explain your thought process- if you don't get the answer right, it might not matter. It's about how you got to it. They also want to see that you are open to suggestions and will rethink your answer if given more information. If they ask you to reconsider and push you in another direction, consider your options and explain why you may or may not change your answer. In order to impress them, it really depends on the college/ people interviewing you. Let your personality come through, and your real passion for your subject. Answer every question they ask even if you don't have the 'correct' answer and stay confident in yourself.