Green’s Dictionary of Slang

jackdaw n.

a jaw.

1858		A. Mayhew Paved with Gold 169: In this curious language did they defy each other, speaking of the jaw as a ‘jackdaw,’ calling an arm a ‘five-acre farm,’ and terming a nose an ‘I suppose’.
1960		J. Franklyn Dict. of Rhy. Sl.
1972		Dodson & Saczek Dict. of Cockney Rhy. Sl. 30: jackdaw. Jaw; as in: A slosh under the jackdaw.