Maybe Durham should be added to the list in my original posting . . . but probably not the rest. No probably not Durham either. With few exceptions UK universities are underfunded. Best to look at the American system if she can't get a spot at the top three or four.

But then that depends on how able your niece is. If her goal is to study at a UK university then best to apply to a range with some of what are called "safety schools" from jjj75's list.