The Metropolitan Police are London's officers, based at Scotland Yard in The Strand. They react to the crimes you commit in the street, but through Frederick Abberline they are also allies who want the Blighters arrested.
Sergeant Abberline asks the twins for help in Abberline, We Presume, and from then on you can capture Blighter targets and hand them over to the police. In the Jack the Ripper expansion, Abberline leads the hunt for the killer in 1888.
If officers keep getting involved in your fights, Police Bribes is the gang upgrade that makes them look away.