The Finding by Nina Bawden
Since nobody knows Alex's birthday (he was found abandoned, at the age of 5 months next to Cleopatra's Needle on the Embankment), he celebrates his finding day every year. On his eleventh finding day, Alex's gran takes him to visit old Mrs Angel, her neighbour, who gives him a photo of a girl in an old photograph frame. The girl in the photo, Mrs Angel's daughter who disappeared years ago, looks a bit like Alex. When Mrs Angel dies a few days later, it is discovered that she has left a fortune to Alex. Mrs Angel's nephew, her only relative and an extremely nasty man, is furious. Soon the local papers get hold of the story and Alex's family is pestered by reporters. Eventually Alex can't bear to see his mother so upset and, feeling it's all his fault, he runs away. After an adventures which becomes frightening, Alex is reunited and everything is sorted out.