Green’s Dictionary of Slang

twirl, the n.

[1950s–60s]

1. (UK Und.) working as a fraudulent bookmaker, typically taking large bets but putting them down on a less popular horse – if the originally betted horse wins, the bookmaker simply claims the bettor was mistaken.

2. a confidence trick that involves the substitution of a fake jewel for a real one.

In phrases

on the twirl

[1930s] working as a professional thief.