The Stray by Dick King-Smith

On her seventy-fifth birthday, Henny Hickathrift leaves the old-folks home with its 'boring people' and sets off on a journey that lands her in the seaside resort of Saltmouth, with all but one penny of her 50 pounds spent. When she spots a stray dog on the beach, she writes in the sand, matter of factly and without a trace of self-pity, 'I am a stray old woman.' A family of five red-haired children spot her message and quickly invite her home, where even their dubious father is charmed by Henny's delight in everything she finds and by her straightforward sense of loyalty and honor.