Green’s Dictionary of Slang

1. a snack, eaten between meals.

1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue n.p.: Damper, a luncheon, or snap before dinner, so called from its damping, or allaying the appetite.
1811		Lex. Balatronicum.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.
1839		Crim.-Con. Gaz. 18 May 160/2: It was Mr Handel’s usual custom, when engaged to dine out [...] to take a little of something by way of refreshment, and to operate by way of a damper, that he might not display his vast powers as a gourmandizer among people of puny appetites.

2. a glass of porter, used as a balance to a glass of spirits; any drink.

1821		Egan Life in London (1869) 266: Now and then a ‘clap of thunder,’ with a damper to make all cool again.
1841		‘F.L.G’ Swell’s Night Guide K3: Cooler, or Damper, a glass of porter.
1899		A. Binstead Houndsditch Day by Day 80: Talking’s dry work, William [...] come and have a damper.
1900		Sporting Times 21 July 2/5: Have a damper?
1921		N&Q 12 Ser. IX 466: Damper (Have A). Have a drink.

3. (UK society) the bill in a restaurant.

1909

J. Ware Passing Eng. of the Victorian Era 103/2: Damper (Soc., 1886 on). A dinner bill – a document which has steadily increased in importance through many years.