Tom's Midnight Garden by Philippa Pearce

From chapters.ca:
Tom is furious. His brother, Peter, has measles, so now Tom is being shipped off to stay with Aunt Gwen and Uncle Alan in their boring old apartment. There'll be nothing to do there and no one to play with. Tom just counts the days till he can return home to Peter.Then one night the landlady's antique grandfather clock strikes thirteen times leading Tom to a wonderful, magical discovery and marking the beginning of a secret that''s almost too amazing to be true. But it is true, and in the new world that Tom discovers is a special friend named Hatty and more than a summer's worth of adventure for both of them. Now Tom wishes he could stay with his relatives and Hatty -- forever...