For what it's worth here is what I'd do with these numbers.
0.08% x population of c60M = 48,000 deaths per month = 1600 deaths per day in a "normal winter".
Pre Omicron, say 1 in 100 people has Covid at any one time. That means that even if Covid didn't actually kill anyone, 16 people per day would die "with Covid" and be included in the numbers. But if official Covid numbers are running at 100 a day, and someone tries to argue that this is not the real number because of this "with Covid" issue, then I'd reject their argument because maybe actually only 84 people are dying "of" Covid, but so what, 100 or 84 is not a big difference. And also, assuming the background prevalence is staying very roughly around 1 in 100, then if the official numbers go up or down I'll take it as reasonably likely that the increase or decrease is "real". In fact even if the background prevalence doubled to 1 in 50, then it doesn't produce a massive shift in the recorded numbers (they "artificially" shift from about 100 to 115 or so).
However...say, in the Omicron era, 1 in 10 people has Covid at any one time. Then, even if Covid doesn't kill anyone, doing the same sums, 160 people per day die "with Covid". Now, if someone says to me that the official numbers indicate, say, 200 "with Covid" deaths per day, but 160 of these probably actually died of something else, I no longer feel I can say "so what" because now it's plausible that in fact a very large proportion of that 200 have in fact died of something else, and just happened to have Covid at the time.
At the moment we are looking at a 7-day average of about 235, up from an average of around 115 that was relatively stable through most of December.
If someone tries to tell me that those additional 120 deaths per day are mostly just an artefact of the greater background prevalence of Covid, then I find that difficult to write off entirely. It seems plausible to me that at least some of it can be explained this way.
The main way in which the argument would fall down of course is if the prevalance in the group of people who have died is a lot lower than it is in the general population. And if we assume that people dying tend to be in older age groups then yes, this is significant.
Looking at the graphs in the ONS survey that
elbows linked to does suggest that prevalence ranges from about 2.5% in the over 80s, rising to about 5% once you get to 60 year olds.
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So I guess that my conclusion would be that the increase we can see in the (28 days/with covid) death rate over the past couple of weeks is, plausibly, influenced by the large rise in background prevalance, but this probably doesn't account for all of it.
(If we re-do my sums in the first bit of this post assuming we are looking at prevalence in, say, over-70s instead of the general population, we could say that pre Omicron, incidental covid deaths might have been 5 per week, and post Omicron, 50 per week)