The link in post #1 says her previous school was Warrender Park in Edinburgh. She was only at Hanover Street School from 2 Jun 1890 to 18 Oct 1890. It doesn't look as though it was a boarding school, and it wasn't a private school either, so not much like in A Little Princess. Here is a picture of it:
https://www.lookandlearn.com/history...l-in-Islington