Green’s Dictionary of Slang

of a mix of warmed or chilled alcohol, i.e. with/without sugar.

1835		Dickens ‘Miss Evans and the Eagle’ in Slater Dickens’ Journalism I (1994) 229: Two glasses of rum-and-water ‘warm with.’.
1838		Crim.-Con. Gaz. 22 Sept. 35/2: [He] had de imperance to toss Massa Crow [...] for a glass of warm wid or cold widout.
1840		R. Barham ‘The Lord of Thoulouse’ in Ingoldsby Legends (1847) 189: An excellent man, / One who stuck to his can / Of cold water ‘without.’.
1848		Sam Sly 9 Dec. 1/3: An incredible number of glasses of stout — hot with — cold without — [...] are consumed.
1861		(con. 1840s–50s) H. Mayhew London Labour and London Poor I 297/1: If any lady or gentleman’ll stand treat to a glass of brandy and water, ‘warm with,’ I’ll tell more about this ‘Rambler.’.
1909		J. Ware Passing Eng. of the Victorian Era 259/1: Warm with (London Taverns). Refers to orders for spirits and water, the ‘with’ refers to sugar.