Boarding school is great you should enjoy it, some people will tell you it's horrible but ignore them - everyone has their own experiences. In terms of what to take, the school should give you a list of everything you will need, and then if you feel you want to bring anything on top of that then do so. I've never been to Chelsea IC but from what I know it's very small and it's location is fantastic, a few minutes to King's Road, pretty much anything you will need is on your doorstep.