Agree re: Jane Gardam! A Long Way from Verona especially.
Get her some virago books.....and Colette.
Roald Dahl's adult stories
Chaim Potok- Asher Lev, The Chosen, In the Beginning, Davita's Harp
Lynne Reid Banks- One More River, An End to Running, The L Shaped Room
Steig Larsson maybe?
Donna Tartt
Simone de Beauvoir- The Mandarins, Memoirs of a Dutiful Daughter, She Came to Stay
Patrick Leigh Fermor
John Fowles- The Collector
A Little History of the World and The Story of Art by EH Gombrich
Mrs Arris goes to Paris and the Elegance of the Hedgehog
The Piano Shop on the Left Bank
The Road Less Travelled
The Moon and Sixpence
Nick Hornby
Cynthia Voigt
Sylvia Plath- Johnny Panic and the Bible of Dreams, The Bell Jar
Jean Rhys- Quartet, After Leaving Mr. Mackenzie, and of course Wide Sargasso Sea
Mitford books- Hons and Rebels, Love in a Cold Climate, The Pursuit of Love, biographies and memoirs etc
Christiane F's book written by journalists
Huckleberry Finn- such a fantastic book. Just float away for an afternoon.
Jonathon Strange and Mr. Norrell
The House of Sleep
Isabel Miller- Patience and Sarah and she's written others too
Jane Bowles- Two Serious Ladies
Margaret Attwood- Cat's Eye
White Oleander perhaps
Lost Illusions- Balzac
A.S.Byatt- The Children's Book, Ragnarok, Still Life, The Virgin in the Garden (all the Frederica books)
A Home at the End of the World
Henri Murger- Scenes from the Latin Quarter
A Very Short Introduction- just pick the ones she vaguely likes the look of....
Far from the Tree- Andrew Solomon
Girl, Interrupted
The Company They Kept: Writers on Unforgettable Friendships (New York Review press)
Cities of the Interior- Anais Nin
The Secret Self: A Century of Short Stories by Women, edited by Hermione Lee
Sophie's Choice
The Reappearance of Sam Webber
Frost in May- Antonia White
The Red Flag: A History of Communism by David Priestland
The Fountain Overflows- Rebecca West (anything by her)
Maupassant, short stories (find a collection with Boule de Suif in)
Wild Heart: Natalie Clifford Barney and the Decadence of Literary Paris- Suzanne Rodriguez
I don't really read that much fiction anymore, so I've just been looking at my bookshelves and picking random titles that might appeal to anyone to put down! Don't know what kind of history your niece is interested in so haven't really put many history books down but I could recommend some if she has a general interest....and likewise if she wants some good biographies of random people 
do come back and update us on your book haul! happy browsing!