Hi heathgirl,
You don't specify the period of time, but in general if you give them details of your relative (Contact at
http://www.mullers.org/), they will be able to tell you if that person was there and you can purchase their records.
They seem to have revamped their website so that's worth checking out too. I haven't really looked at the new one yet, but it seems to have some interesting historical photos.
My relative was living in Devon when she was admitted, so why not Kent. The census might help but, at least on the 1861 census, it seems that they recorded the children by their initials only, so it's not so easy to identify them, as you only have the initials (e.g. M S F in my case), age and place of birth to go on.
I'm not sure if there was a C of E connection : I think George Mueller ran this as a private institution and in many ways he went "against the grain" of the times. His story is very interesting and well worth reading, either on their website or even wikipedia (
http://en.wikipedia.org/wiki/George_M%C3%BCller.
Best wishes,
Alan