Looking for children’s/teen book read ~15 years ago

I think I read this in the early 2010s, paperback, fairly short. Cover was maybe purple with a black silhouette of a girl (maybe just her hair/silhouette). Main character’s name was Violet I think. (Vague) plot I remember: boy saves a dog from a river/lake. The girl in the story sends him a letter and they write back and forth before meeting up. Young teens, probably small-town UK setting. Not illustrated inside. Any ideas?