I know I am good at maths, but is there anything more I need to do in my interview to secure a place to study it?

Oxbridge admissions tutors are not looking for someone who is good at maths at school, they are looking for someone who will thrive studying mathematics at university. These are often two very different things. First of all, you don't need to worry about being a well-rounded person, or knowing all sorts of interesting mathematical fact bites. Instead, make sure you understand the old material - ask questions about it, try and confused yourself with it, use old tools in new and curious ways. Mathematics at Oxbridge will puzzle you - but it shall be all the more enjoyable for it. Secondly, interviews are like tutorials: what you are experiencing now will be what you will experience every week, perhaps five times a week, if you get into Oxbridge. Thus, try and enjoy it! Although you are likely to be nervous, and obviously wanting to do as best you can, the tutors want to enjoy teaching you, and you to enjoy being taught - so give it a go!