Green’s Dictionary of Slang

1. to make tea in a billy-can or similar container.

1930		(con. 1914–18) Brophy & Partridge Songs and Sl. of the British Soldier.
1931		E. Blair letter 4 Sept. in Complete Works X (1998) 228: As to new words, here are some [...] Drum up, to = to make a fire.
1933		M. Marshall Tramp-Royal on the Toby 6: Taking my drum from my peter I dip it in the pool [...] and set it on the blaze. Then, I drum-up.
1933		(con. WWI) F. Richards Old Soldiers Never Die (1964) 26: Some [of our men] were drumming up – that is, making tea.
1939		J. Worby Spiv’s Progress 9: I’m going to drum up first .

2. to prepare a meal under rough conditions (typically on a battlefield or out of doors).

1936		J. Curtis Gilt Kid 202: They carries their stuff about with them. A spare shirt and a couple o’ tins in case they want to have a shackle up. But you can’t drum up in London.
1937		J. Worby Other Half 220: I was drumming up on the outskirts of a small village.
1943		R. Llewellyn None But the Lonely Heart 351: You can drum us up a cup when we get in.