Given the lengthy introduction citing numerous hyperbolic warnings about the primarily negative and potentially disastrous health effects anticipated due to climate change, it is mildly amusing (though hardly surprising to anyone familiar with the literature) that they observe that temperature-related mortality has decreased sharply over the interval studied. More interestingly, they find that a major cause of this decrease is not even the warmer winters the UK has seen, but rather better adaptation to cold weather. This of course directly refutes the "optimally adapted" meme, since if that was the case, we would expect to see a decrease rather than the observed increase in tolerance to cold extremes as the winters got warmer. But in reality, wealth and technology (eg insulation, heating and clothing) act to increase our tolerance whether or not the climate changes, although the latter may in theory act as an additional stimulus if it were sufficiently important (which it clearly is not, in the UK).
Of course they have to finish off by talking about increases in heatwaves, wondering "whether adaptation will manage to keep pace with such changes". I think it is patently obvious that it will, and would happily bet against any predictions of increasing temperature-related deaths in coming decades.