The Broughton Hall I recall is a Catholic Girls High school, in Honeysgreen Lane, West Derby.
The next door school is now Cardinal Heenan High school for boys and this was originally the orphanage from about 1870.
The School is now to be knocked down and rebuilt.
I presume from this, that the orphanage would have been run by nuns.
I tried googling but didn't get very far.
Hope this helps a bit.
Olly