There is also A School for Magic by Caroline Stevermer (okay) and Sorcery and Cecilia by Caroline Stevermer and Patricia Wrede (excellent). Both have sequels. These have girl protagonists, magic, and that British feel, though the later lacks a school.
Terry Pratchett’s The Wee Free Men has magic and a girl protagonist, but lacks a school setting, as do all of Robin McKinnley’s books (the latest, Sunshine is post-apocalypic. The rest are traditional fantasy. Witch Week by Diana Wynne Jones has a school, magic, and is British, but there are several protagonists, some of which are female. I think the original “Song of the Lioness” books by Tamora Pierce are superior to the later books (Alana: The First Adventure, In the Hand of the Goddess, The Woman Who Rides Like a Man and something else).
I will probably think of some more.