Birmingham Alley

above from skyshaper
More on Birmingham Alley, which no longer exists but which at one time linked Henry and Madison Street. Shown above is the corner of Madison and Mechanic's Alley (formerly Birmingham)
from Bowery Boogie

Mechanics Alley is one of the skinniest streets in NYC, still running east to west between Cherry and Henry Streets, and north to south between Pike and Market Streets. The section of the alley between Henry and Madison Streets was known as Birmingham Alley. The original Mechanics Alley ran only between Cherry and Monroe Streets directly under the Manhattan Bridge, not just south of it (as it is today, on the path of the old Birmingham Alley). The original Mechanics Alley disappeared after 1905 when the Manhattan Bridge was constructed. There was a Mechanics Place behind 359 Rivington Street between Lewis and Goerck Streets.
Builders who worked as artisans, artificers, craftsmen and tradesmen were once called mechanics. Because they had the skills to build new settlements, mechanics who immigrated to the New World in the 17th century were promised free ship passage, free land, and exemptions from taxes and military service. Carpenters, bricklayers, masons, glaziers, painters and plasterers came to NYC and received great wages as they built and rebuilt the constantly growing city.

on the name origin of Birmingham Alley? The English city name origin:

There are many theories and we will never really know where it came from. However, most people argue that the name 'Birmingham' comes from "Beorma inga ham", "meaning farmstead of the sons (or descendants) of Beorma"
Beorma variously means, in Old English, "fermented", "head of beer", "yeasty" or "frothy",[4] from which the modern English words barm and barmy are derived.[5] The assertion that Beorma was the founder of Birmingham arose from a post-war challenge to the way Anglo-Saxon place-names had been constructed. It was not until 1940 that Eilert Ekwall noted that.