I believe the Sophia you saw at Watford was married to Joseph Stead who came from Nottinghamshire. Sophia was born Badgeley, Warwickshire so this is not your girl.
Just checked the addresses in 1851 and 1861, although difficult to read for me, I believe they were different streets.
As for the IGI I wouldn't like to say at this point, although a good possibility, however, I am not sure how good the coverage actually is.