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 Needlemaker's Company bore in their arms. It begins from the Mansion House, and therefore the Bank stands in it.
“A silver curl-paper that I myself took off the shining locks of the
ever-beautiful old lady of Threadneedle Street [a bank-note].” —
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894