Brewer's: Finch Lane
(London). So called from a family of consideration by the name of Finch or Finke. There was once a church in the lane called St. Benet Finke. There is an Irish saint named Finc, in Latin Fincana, whose day is October 13th.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894