Reading the article*, that's not exactly what it says - Minimum Mean Temperature is that at which the fewest people die, so you could just as easily flip it on its head and say that below 17° more people will die too. I won't be panicking myself, and I am certain that this means it is behaviour-driven, not that people in this country drop like flies at so low a temperature!
I suspect a part of how this works in terms of cold (probably only a very small part) would be that we don't mandate winter tyres, so in very cold conditions we probably have more car crashes and therefore more deaths on the road during such conditions.
Similarly in terms of very hot weather, air con/ceiling fans are largely absent in UK buildings, and we are geared towards keeping heat in our buildings, not out.
*Started typing this after you posted!
The bottom line is that the shape of the curve would tell a lot - I suspect that either side of 17° the gradient is almost invisible - it would be interesting to know where it properly begins to steepen.