Green’s Dictionary of Slang

tosh n.²

a hat.

1890		Sporting Times 1 Feb. 2/1: ‘So convenient a stormy Channel passage, isn’t it? Gets rid of beastly old hats in a lovely manner, don’t it?’ Still, I am not a person to be put down by idle clamour, so I stick to the tosh.
1903		A. Binstead Pitcher in Paradise 194: I pulled myself togther, set my tosh on a bit straighter, an’ sent my card up to the C.O.