I was puzzled when I saw your post and looked at the paper in question you provided. All of the data sources the paper cited for this chart seem to begin in 1800 rather than 1530. Specifically Riley (2005) (pdf) is the source for 19th Century data he gave. So honestly I haven’t got a clue what we are looking at for earlier data, though I suspect it might be estimated for a specific region, as records are quite bad (especially for poor people) going that far back. These types of estimates often infer from sub-populations, and are usually inaccurate enough that it is irresponsible to represent exact year-by-year numbers. That’s why in Riley’s paper he gives data only for each decade. So I’d dig into your data deeper and see what is actually being used to infer UK mortality before 1800.

As u/Prosodism said - the sources are not very clear on the ultimate origin of the data. But I suspect that it comes from Wrigley and Schofield's population history of England. In any case it seems fairly certain that it must derive from the same primary data that they used - the Anglican parish registers which were kept since 1538. These registers record baptisms, marriages and burrials in about ten thousand English parishes. This is a fairly complete, although far from ideal, record of English vital statistics.

The exact decline in LE seems to be in the period 1553 to 1558 - the reign of Mary. While it is possible her reign actually did lead to higher mortality, we also know that this period had an especially high percentage of defective burial registrations. It is possible that the extreme difference is partially accounted for by the poor qualtiy of the data.

Wrigley and Schofield actually have a discussion though of extreme mortality crises (page 332) and they do highlight 1558 as having unusually high mortality (as well as 1728 the other dip in the graph). The former may be related to infectious disease which Webster (1979) says could have been a variety of influenza. His argument is that mrtality in these years was connected to famine conditions and malnutrition in the preceeding years. 1557 and 1558 appear to have had generally good harvests, but many of the deaths probably occurred before the reduction in food price in late 1557. The large number of deaths might mean that the period between death and burial was longer, making the deaths look a little later, but that is mostly speculation on my part.

The 1728 mortality also very much looks to be famine related (Klemp and Weisdorf, 2012).

Prior to modern medicine, market economies and democratic government - famines were frequent and lead to major spikes in mortality. The main killers were epidemic diseases that were more deadly in a malnurished population (actual starvation was not usually the killer). Even as late as 1918 the influenza epidemic of that year had a noticable impact on mortality, which in graphs is often mistaken by people as being WW1 casualties.

Of course it seems odd to say life expectancy declined. If you survived the bad year your life expectancy going forwards would not be so dramatically impacted (Klemp and Weisdorf's article is actually about the longer term health impacts on new borns). However, the way we calculate LE is to take an imaginary cohort and subject them to all the age specific mortalities - so the LE is kind of like saying your expected length of life if you lived your entire life in the mortality conditions of that year. So the series is not so much telling you expected length of life (it's also an average that is heavily skewed by infant deaths, if you survived childhood you had a decent chance of living to 60) it is more telling you about years of mass mortality.

Wrigley, E. A., Schofield, R. S., & Schofield, R. (1989). The population history of England 1541-1871. Cambridge University Press.

Webster, C. (Ed.). (1979). Health, medicine and mortality in the sixteenth century (Vol. 1). CUP Archive.

Klemp, M., & Weisdorf, J. (2012). The lasting damage to mortality of early-life adversity: evidence from the English famine of the late 1720s. European review of economic history, 16(3), 233-246.