Are you sure on the parents' names?
I see an Alfred and Annie of those ages on the 1871 census in Lambeth but to a William and Emily (Emily listing herself as b. France), and with more siblings. There is also a baptism for a Annie Lake at the British Chapel in Lille, parents William Lake and Emilie.
Her birth is in the French civil records (indexes) as Annie Emilie Lake, b. 23 Jan 1860, as are younger siblings, Elizabeth Antoinette (b. 14 Jan 1863), Edouard Henri (b. 2 Jan 1865), and Clara Felicie (4 November 1867), but Annie's birth shows her mother as Marie Josephine Emilie Malfoy.