Green’s Dictionary of Slang

to share lodgings or diggings n. with.

1910		Wodehouse Psmith in the City (1993) 41: I have omitted to ask you where you are digging.
1914		C. Holme Lonely Plough (1931) 106: He digged in my hotel when he had the cash.
1915		G. De S. Wentworth-James Purple Passion 39: It’s mouldy living alone. Besides, I could go and dig with Chrissie and make a bit on letting the flat.