Green’s Dictionary of Slang

a Bow Street runner.

1825		Pierce Egan’s Life in London 3 Apr. 80/3: The Patrol [...] have to provide themselves in decent attire, with the addition of a fine scarlet waistcoat.* [note] *Slangly termed Robin Redbreasts.
1833		‘Poll Tomkinson’ in Convivialist in Spedding & Watt (eds) Bawdy Songbooks (2011) IV 14: For the robin by a red breast he vos took avay.
1834		Westmorland Gaz. 14 June 1/3: He [...] presently comes in with a robin-redbreast in tow, who says to me says he, you’r [sic] the man wot boned the man’s razors.
1843		R.S. Surtees Handley Cross (1854) 290: In less than five minutes the red-breasts* - for it was before the crusher times - were flow. [Footnote *The Bow Street officers of former times wore red waistcoats].
1862		Dickens letter 18 Apr. in Letters (1880) II 178: The Bow Street runners [...] had no other uniform than a blue dress-coat, brass buttons [...] and a bright red cloth waistcoat. The waistcoat was indispensible, and the slang name for them was ‘red-breasts,’ in consequence.
1873		Sl. Dict.
1881		Salisbury Times 9 Apr. 6/2: The Bow-street runners or —as they were named from their red plush waistcoats — ‘Robin Redbreasts’.
1914		(ref. to late 19C) Dly Gaz. for Middleborough 9 Jan. 2/5: Twenty-five years ago there were still surviving ’robin redbreasts’ [...] calling out [...] ‘Bow-street patrol’.