The Railway Children by E. Nesbit

When Roberta, Peter and Phyllis's father is imprisoned after being falsely accused of spying, they and their mother have to leave their comfortable London home to go and live in a small house in the country. However, the children soon come to love the railway that runs near their cottage, and have many adventures - stopping a train from disaster, saving an infant and dog from a barge canal on fire, and getting help when they find an injured boy in the trail tunnel. When they befriend an Old Gentleman who regularly takes the 9:15 train near their home, he helps them to prove their father's innocence, and the family is reunited at last.