I managed to get through the first two papers -- which, incidentally, date back to February, so maybe it's a little surprising to see them in news now as opposed to then. They were, I think, reported on in various media outlets at the time.
I'm not sure how persuasive they are, or should be. It's not difficult to find passages scattered in both papers that make it easy to imagine at least some amount of politics driving the conclusions reached. For example, there's this passage at the end of the second paper:
"Yet, despite claims by some current cabinet ministers that leaving the EU would generate an extra £350 million per week for the NHS, the government reportedly has no plans to increase funding."
Now, I'd happen to agree that Johnson in particular seems determined to repeat this claim, writing in the Telegraph a couple of months ago: "Once we have settled our accounts, we will take back control of roughly £350m per week. It would be a fine thing, as many of us have pointed out, if a lot of that money went on the NHS..."
But the main point is that including such a line in the paper does come across as very politically motivated, and I wonder how easy it is to separate the analysis from the politics. Such is always the problem with statistics. Numbers don't lie, but the people reading them may do.
I would also like to see the full critiques from someone called Jones and another person called Eugene Milne, both of which -- along with the authors' reply -- are blocked behind a wall I can't seem to get past even through the university. But Milne (http://journals.sagepub.com/doi/full/10.1177/0141076817703881 ) notes, and I concur, that "the visual appearance of a rise [in mortality rate since 2010] is heavily dependent on the 2015 data point."
So, I don't know. If the reported trend continues for a few more years, then it's hard to argue against the idea that something has changed very recently such that older people are at greater risk of death than previously. But it's tricky to know what to attribute that cause to. Despite what NJ says, austerity has actually been a thing for the last few years, so it certainly *could* be a knock-on effect of government policy. But I don't think the papers are definitive enough on this.
To be fair, the authors are careful not to state any definitive conclusions either.