Wikipedia search recommended! It comes from a UK law called the Riot Act granting officials the power to forcefully disperse gatherings if they refuse to disper

Wikipedia search recommended! It comes from a UK law called the Riot Act granting officials the power to forcefully disperse gatherings if they refuse to disperse after a verbally delivered warning - the precise wording of which was specified by the Act. So an official would literally read the Riot Act to a troublesome group, and if they kept it up, the lads with truncheons would come and start cracking heads. The idiomatic transfer is fairly obvious, although the implication of consequences if the admonished party is insufficiently contrite has become sort of optional, I think.