The Millbank Penitentiary was conceived by a reformer, Jeremy Bentham, and intended to replace a brutal and disreputable system with one more humane. The concept caught on in the U.S., and the Eastern State Penitentiary, which still stands, was built in the same decade.
Thomas Allen, in The History and Antiquities of London, (1839), expresses a less than heartening opinion of the place, when it wasn’t yet 20 years old.
And here it is on an 1830 map of London, (click on Map & Page Grid and you'll find it in the lower left quadrant).
Illustrations from Henry Mayhew & John Binny, The Criminal Prisons of London, and Scenes of Prison Life, 1862