Background A series of public health interventions, alongside progress in health and in living conditions, in industrialised economies during the second half of the 19th century and the early decades of the 20th century catalysed technological change that led to very large reductions in mortality. For example, data we have compiled from municipal records show that in London, the largest city in the UK around 1900, the annual crude death rate fell, respectively, from around 24 deaths per thousand before the 1850s to about 13 deaths per thousand in the 1930s, without further appreciable reductions in the following decades. This historical episode, often referred to as the mortality transition, has been studied over several decades and generated a large literature.

Methods First, we analyse empirically the dynamics of the reductions in the death rate over the period of the mortality transition using the long time series of the crude death rates that we have constructed for London and its constituent areas. Second, we examine empirically the monotonicity of the convergence of mortality rates by socioeconomic conditions, by testing the theoretical prediction of the dependence of the inflection point on the income distribution, using data for the administrative areas of London.

Results Firstly, we estimate trend mortality for each area and find that, in general, reductions of the death rates over the mortality transition period are characterised by a sigmoid pattern in the form of a logistic function. The inflection point of trend mortality, associated with the change in the convexity of trend mortality and the highest rate of mortality reduction, occurs around 1900 at the city level. However, the timing of the inflection point differs between the areas of London, implying substantial differences between these areas in terms of the length of the periods of slow and rapid reductions in mortality, with the timing of the beginning of the period of rapid declines differing in some cases by several decades. The differences between areas suggest that started with lower mortality also typically experienced reductions in mortality earlier (by 3-10 years, p < 0.01).

Conclusion Our results demonstrate that technological progress and advances that generated one of the most celebrated episodes of improvements in human well-being only did so via a substantial and prolonged increase in health inequalities. Thus, although the socially desirable progress of the mortality transition benefited the vast majority within a century, the inequality impacts were considerable over a period of several decades.