Green’s Dictionary of Slang

alligator adv.

later.

1960		J. Franklyn Dict. of Rhy. Sl. 32/1: alligator Later [...] of 20 C. origin.
1969		S.T. Kendall Up the Frog.
1992		R. Puxley Cockney Rabbit.
2001		M. Coles Bible in Cockney 83: Now time was getting on, and a little alligator his disciples came up to him.