An Elephant in the Garden by Michael Morpurgo
Lizzie and Karl's mother is a zoo keeper; the family has become attached to an orphaned elephant named Marlene, who will be destroyed as a precautionary measure so she and the other animals don't run wild should the zoo be hit by bombs. The family persuades the zoo director to let Marlene stay in their garden instead. When the city is bombed, the family flees with thousands of others, but how can they walk the same route when they have an elephant in tow, and keep themselves safe? Along the way, they meet Peter, a Canadian navigator who risks his own capture to save the family.