Green’s Dictionary of Slang

1. wig.

1972		Dodson & Saczek Dict. of Cockney Rhy. Sl.
1981		P. Wright Cockney Dialect and Sl. 106: Irish jig ‘wig’.
1983		J. Byrell (con. 1959) Up the Cross 146: He’d once tried covering his baldness up with one of those expensive Irish jigs.
1992		R. Puxley Cockney Rabbit.
2002		B. Kirkpatrick Wicked Cockney Rhy. Sl.
2019		P. Baker Fabulosa 293/2: Irish a wig.

2. (Aus.) a term of abuse for an Irish person, a pig.

1968

J. Alard He who Shoots Last 95: ‘You will, ya big Irish Jig!’ ‘Who ya callin’ a pig? [...] ya little pest!’.

3. a cigarette [cig n.].

1981

P. Wright Cockney Dialect and Sl. 92: cigarettes ‘Irish jigs’.