Green’s Dictionary of Slang

birch broom n.

a room.

1857		‘Ducange Anglicus’ Vulgar Tongue.
1864, 1867, 1870		Hotten Sl. Dict.
1873		Sl. Dict.
1910		Eve. Teleg. (Dundee) 3 Aug. 4/1: Few landladies would understand [...] 'What birches do you have to let?' This refers to brich brooms [...] 'rooms'.
1946		St. Vincent Troubridge ‘Some Notes on Rhyming Argot’ in AS XXI:1 Feb. 47: shovel and broom. A room. (Origin uncertain, American or English.) May be American. If British, it is much rarer than birch broom.
1960		J. Franklyn Dict. of Rhy. Sl. 39/2: birch broom Room [...] now seldom heard, since birch-brooms are no longer used. Birch broom in a fit, for disordered hair is more common.
1969		S.T. Kendall Up the Frog 20: I’ve got a birch broom rahn the Johnnie ’Orner.