Green’s Dictionary of Slang

rod (and float) n.

an overcoat .

1915		Dly Mirror 1 Sept. 10/3: ‘A rod’ is a shortening of ‘rod and float’ which is rhyming slang for overcoat.
1930		(con. 1910–20s) D. Mackenzie Hell’s Kitchen 120: Rod ... overcoat.
1938		F.D. Sharpe Sharpe of the Flying Squad 332: rod : An overcoat or mackintosh.
1977		D. Powis Signs of Crime 199: Rod Overcoat.
1989		J. Morton Lowspeak.