Chapter 2 of Providence focuses on Kitty's university life. Both she and her lover Maurice have flats in London, from where they commute to their 'provincial' university; we are told the financial supporters of the institution, the Friends, hail from the 'surrounding countryside'.
I suspect Brookner means Reading. She was a visiting lecturer at the University of Reading from 1959 to 1964. It gives Providence a particular, perhaps rather charming non-Londoncentric air. Campus life, the provinces: this could be David Lodge.