That's one of the things I admire most about British English: it does tend to be less childish the American English and to have resisted the encroachment of some of these words.

I don't known British slang and colloquialisms well enough to have dealt with them in my story. But my impression (from reading U.K. media) that "willy" is in the same category with "tummy." It seems a respectable word for "penis" in Britain but might sound childish here.