E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
I must send you to Birchin Lane, i.e. whip you. The play is on birch (a rod).
A suit in Birchin Lane. Birchin Lane was once famous for all sorts of apparel; references to second-hand clothes in Birchin Lane are common enough in Elizabethan books.
Passing through Birchin Lane amidst a camproyal of hose and doublets, I took occasion to slip into a captains suita valiant buff doublet stuffed with points and a pair of velvet slops scored thick with lace.Middleton: Black Book (1604).