A copy of one of Charles Booth's London Poverty maps in my collection
Many of my ancestors ended up in London. The city was a draw for people from all over the country. Just off the top of my head I can think of at least three places that I've been able to document that my ancestors hailed from: Dorset, Suffolk, Essex and Norfolk - oops that looks like four that automatically came to mind. Because of this, I've amassed books on London, its history and social issues. Among the collection are also London atlases from various time periods as well as the Poverty Maps that Charles Booth drew up in 1889. While Sarah died a few years before that date, I think that those maps will be a good indicator for the state of the areas she lived in even if that happened to be decades earlier. I don't think there was much reform prior to Booth bringing the state of London's areas to public notice.
I have amassed a list of addresses for Sarah from official government documents such as marriages and deaths as well as census information. Also helpful for tracking down the family's moves were baptismal records. I wasn't able to find those for all 9 of the children and, in the case of 3 of the offspring, they were all baptized in the same month and year, so that source wasn't as helpful as hoped but there are still a lot of moves and changes of abode to cover. Now to track the places on a map if I can find them all.
Sources:
GRO certificates for marriage and deaths obtained from the General Register Office in the UK
Parish records accessed through Ancestry and FindMyPast