Wellcome Library is full of many wonderful things. Among its treasures are the Medical Officer of Health reports, which span the period 1848-1972. These have now been digitised and are freely available on its website.
So what's in them? For any central London area, you can see how many people got sick, what they caught, how many died and how many were born in any given year. To take one illustrative example, at a click, you can now find the causes of death in Hackney in 1864. Among many ailments, 79 people died of measles, but only 2 of influenza. 239 succumbed to bronchitis and 128 to pneumonia. Six unfortunate children died for 'want of breast milk', and 12 people drowned. And so on. You might then compare these statistics to those of other boroughs, or in the same borough across time — with the caveat that the data were never fully standardised.
The reports go much further than life and death stats, however. The medical officers also offer insights into many other areas of public health and welfare. To take a few random examples, you can discover: the amounts of free milk distributed in a borough (and those fined for watering it down), new paving schemes, dwelling houses closed to make way for businesses, vaccination statistics, and much more besides. We even discovered that a six-man Victorian urinal used to stand outside Londonist Towers near Old Street.
The many tables and other data are readily downloadable, and the full resource is keyword searchable. Go have a play, and see what you can find for your street or area.