The city Bridewell, Bridge Street, Blackfriars, was built over a holy well of medical water, called St. Bride's Well, where was founded a hospital for the poor. After the Reformation, Edward VI. chartered this hospital to the city. Christ Church was given to the education of the young; St. Thomas's Hospital to the cure of the sick; and Bridewell was made a penitentiary for unruly apprentices and vagrants.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894