I'm not going to lie, I'm no expert on UK law, particularily around ages of emancipation and housing, ect. However, I do believe that you can live by yourself when you're 16, as you can work and pay taxes, ect.
I think that in this context, Gracefield house is used as a bit of a boarding house for the nearby private school, as mentioned. So there must be some kind of contract, between the school, parents of the child and a temporary guardian of the child so that younger students can live there. I presume that they would have to have a legal guardian while in the country, the landlord, perhaps? I hope that answers your question.
And yes, I'm sorry, I'm really bad with spelling. I'll look over it when I get home, I promise.