The London Metropolitan Police was established on September 29, 1829, by Home Secretary Sir Robert Peel. His names provided early nicknames, "Peelers" or "Bobbies," for members of the force. It was the third official non-paramilitary city police force in the world. The predecessors were the City of Glasgow Police (1789) and the Paris Police (1667 –1789 under the monarchy, and reformed under Napolean I in 1800.)
Most police historical references of which I'm aware tend to stress the London “Met” as being “the origin of modern municipal police.” This takes a bit of creative interpretation, but it is accepted useage. There were earlier efforts to provide a police presense in London, but they were not organized on a citywide basis.
London Bobby on traffic duty, 1950s