A street near Moorfields, formerly the supposed habitation of many persons who wrote for the booksellers: hence a Grub-street writer means a hackney author, who manufactures books for the booksellers.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Grub * Grub Street NewsNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes