E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
A corruption of Thryddanen or Thryddenal Street, meaning third street from Chepesyde to the great thoroughfare from London Bridge to Bushop Gate (consisting of New Fyshe Streate, Gracious Streate, and Bushop Gate Streate). (Anglo-Saxon, thrydda or thrydde, third.)
Another etymology is Thrig-needle (three-needle street), from the three needles which the Needlemakers Company bore in their arms. It begins from
the Mansion House, and therefore the Bank stands in it.
The Old Lady in Threadneedle Street. The directors of the Bank of England were so called by William Cobbett, because, like Mrs. Partington, they tried with their broom to sweep back the Atlantic waves of national progress.
A silver curl-paper that I myself took off the shining locks of the ever-beautiful old lady of Threadneedle Street [a bank-note].Dickens: Dr. Marigold.