Historical gains in life expectancy in the past two centuries, much of it occurring prior to the advent of effective antibiotics, were largely a matter of control over infectious disease via public health measures such as sanitation, coupled to a rising standard of living. A sizable amount of the gain in life expectancy at birth is due to reduced infant mortality, but this isn't the whole story. It is worth noting, as in this article from a few months ago, that the data shows remaining life expectancy at all ages heading upward over time. Reducing the burden of infectious disease has effects at all ages, not only due to incidence at a given age, but also by reducing the accumulated damage due to serious infections suffered throughout life.
It's often argued that life expectancy across the world has only increased because child mortality has fallen. If this were true, this would mean that we've become much better at preventing young children from dying, but have achieved nothing to improve the survival of older children, adolescents and adults. Once past childhood, people would be expected to enjoy the same length of life as they did centuries ago. This is untrue. Life expectancy has increased at all ages. The average person can expect to live a longer life than in the past, irrespective of what age they are.
The most striking development is the dramatic increase in life expectancy since the mid-19th century. Life expectancy at birth doubled from around 40 years to more than 81 years. This achievement was not limited to England and Wales; since the late 19th century life expectancy doubled across all regions of the world. The evidence that we have for population health before modern times suggest that around a quarter of all infants died in the first year of life and almost half died before they reached the end of puberty and there was no trend for life expectancy before the modern improvement in health: life expectancy at birth fluctuated between 30 and 40 years with no marked increase ever.
A common criticism of the statement that life expectancy doubled is that this "only happened because child mortality declined". I think that, even if this were true, it would be one of humanity's greatest achievements, but in fact, this assertion is also just plain wrong. Mortality rates declined, and consequently life expectancy increased, for all age groups. In 1841 a five-year-old could expect to live 55 years. Today a five-year-old can expect to live 82 years. An increase of 27 years. The same is true for any higher age cut-off. A 50-year-old, for example, could once expect to live up to the age of 71. Today, a 50-year-old can expect to live to the age of 83. A gain of 13 years.