I was asked to submit work, but not school work as I had expected. I was sent two lists of essay titles and had to chose one from each. I had just less than 10 days to write them both and having never done anything related to sociology or anthropology before it was quite scary! The titles I chose were subject specific (they all were, I chose my favourite and the most quirky!) 'There is no such thing as society. Discuss' and 'To what extent is it possible to distinguish treasure hunting from archaeological investigation ?' So don't assume written work equals essays you've already written!
They were mentioned (only to say they liked them and nice introductory stuff) but I ended up relying on my soc anth essay (society one!) in that interview because I was totally lost on what I was being asked...didn't really understand any of that to be honest, really random and insanely long questions, I had no idea how to answer a question I didn't even understand so just kept refering to points in my essay or any preparatory reading I had to do in order to write the essay! I think she was as confused as I was by the end of it!
If I were in your shoes I'd ask them for a suggestion of an essay title or topic, explaining you're not in school so would rather write a new one! Then they'd have to discuss it with you, or at least be impressed!