Exeter, Birmingham, Nottingham and Southampton were all on my daughter's list, along with Leeds.
Exeter and Birmingham were her top choices and she plumped for Exeter, where she is now very happy. Her predicted grades were not 3 x A* though. With those grades, we'd definitely have been looking at Oxford, Durham and Bristol (like yours, she didn't want Scotland or London).
My daughter decided against it, and it is more competitive, but it would be worth looking at an Integrated Masters. Exeter and Birmingham definitely offer them, and from memory most other places she looked did too.
We found that the course content was much the same everywhere (they have to cover the same core content to get BPS accreditation). The main differences were in options for years out: in the UK and abroad.
And of course as for all students, there are considerations around location and type of university (campus vs town etc) to take into account.