I discovered this through Marjie Bloy's excellent website on English history. She has a lot on Sir Robert Peel and early police (that's how I found it).
During the night they never cease patrolling the whole time they are on duty, being forbidden even to sit down. The police district is mapped out into divisions, these into sub-divisions, these into sections and these into beats, all being numbered and the limits carefully defined. To every beat certain constables are specifically assigned, and they are provided with little maps called beat-cards. The business of the constable on duty is to walk around his beat in a fixed time according to an appointed route. As soon as he has gone over it, he immediately begins his rounds again, so that the patrolling sergeant knows at any moment where the constable ought to be found unless something unusual has occurred. In this way every street, road, lane, alley and court within the Metropolitan Police District is visited constantly day and night by some of the police. The beats vary considerably in size. In those parts of the town that are open and occupied by the wealthier classes, an occasional visit is sufficient but where the character and density of the population is different, the throng and pressure of the traffic greater and the streets intricately designed the frequency of visits is increased. Within a circle of six miles from the centre of Kensington the beats are usually covered in periods varying from seven to twenty-five minutes and there are points which are never free from inspection.
When anything occurs in the district worth communicating the intelligence is conveyed from one constable to another until it reaches the station house, thence, by an admirable arrangement of routes and messengers to the headquarters of the central office in Whitehall. Then it can be radiated along lines to each divisional station-house to every constable. This rapid transmission of intelligence is important as regards the detection of crime but especially as a means of preserving the city from riot. The effectiveness of this was proved with the disturbances of 1832 [the Reform Act riots]. In case of emergency the Commissioners could use this system to collect all 5,500 men in one place in two hours. There has therefore been no need to call upon troops. All crimes have been reduced but, because of this system, especially felonies, assaults and larcenies. Few people now dare carry weapons. Indeed many criminals have moved elsewhere for safety and easier work.