Bow Street runners, who wore a scarlet waistcoat.
“The Bow Street runners ceased out of the land soon after the
introduction of the new police. I remember them very well as standing
about the door of the office in Bow Street. They had no other uniform
than a blue dress-coat, brass buttons ... and a bright red cloth
waistcoat ... The slang name for them was `Red-breasts.”' —
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Red-breasts from Infoplease: