Green’s Dictionary of Slang

billy n.3

[? King William IV, in whose reign (1830–37) the practice began. The silk handkerchief was a central part of costermonger fashion, often aping that of the prize-ring, where fancy handkerchiefs were an essential trademark of certain fighters. As Mayhew notes, in London Labour and the London Poor (1861–62): ‘The costermonger [...] prides himself most of all upon his neckerchief and boots. Men, women, boys and girls all have a passion for these articles. The man who does not wear his silk neckerchief – his “King’s-man” as it is called – is known to be in desperate circumstances, the implication being that it has gone to supply the morning’s stock money’]

[mid-19C] a silk handkerchief, worn by London costermongers.

In compounds

billy buzman (n.) [buzman under buz n.]

[19C] a pickpocket who specializes in stealing silk handkerchiefs.