With regard to the whistle, Ed Snowden described in his memoirs an old naval system of communication with whistles, and in particular how they could be used to signal that there were things wrong with the ship which put it in danger and warranted it promptly being taken to port for rectification.

I don't really have any independent information as to whether that or this present post's reference to Victorian policemen giving chase is more true for the origins of the whistleblower expression, but Snowden's certainly seems more apt for the act.