The Railway Children (Collins Classics)

...when the Green Dragon tore shrieking out of the mouth of its dark lair, which was the tunnel, all three children stood on the railing and waved their pocket-handkerchiefs without stopping to think whether they were clean handkerchiefs or the reverse.'

When their father is mysteriously sent away, Roberta, Peter and Phyllis have to leave London with their mother to live in a cottage in the countryside. Finding comfort in the nearby railway station and friendship in Perks the Porter and the Station Master, the children watch every day for the passing London train. Every day they wave at the same old Gentleman on the train, not knowing that he may hold the key to their father's whereabouts.