For example in November 2022, about 99% of all deaths are in vaccinated people if you take the total number of deaths in England from the ONS user response, but only about 92% of deaths are in vaccinated people if you take the total number of deaths from the spreadsheet which accompanied the article about the new baseline methodology (which is by registration date and not date of occurrence, but it's still closer to the real number of deaths by date of occurrence).
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You speculated that "those susceptible to death had almost all been injected before dying". However I don't think your theory holds water, because in the FOI response there's 269,247 people who died in the second half of 2022, but only 193 of them had received their first vaccine dose on a week that started in the second half of 2022 (whatdotheyknow.com/request/deaths_in_nims_database#incoming-2653782):
Based on the link in your second paragraph, your source for deaths among the resident population of England was this ONS user request: ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/adhocs/1343dailydeathsbydateofoccurrence1stjune2014to31stmay2023bysingleyearofageengland.
The deaths in the user request were by date of occurrence and not registration date, and the response was published in July 2023, so in the second half of 2022 there were still many deaths that were missing because of a registration delay: sars2.net/statistic.html#Plot_where_nearly_100_of_deaths_were_in_vaccinated_people_in_late_2022.
For example in November 2022, about 99% of all deaths are in vaccinated people if you take the total number of deaths in England from the ONS user response, but only about 92% of deaths are in vaccinated people if you take the total number of deaths from the spreadsheet which accompanied the article about the new baseline methodology (which is by registration date and not date of occurrence, but it's still closer to the real number of deaths by date of occurrence).
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You speculated that "those susceptible to death had almost all been injected before dying". However I don't think your theory holds water, because in the FOI response there's 269,247 people who died in the second half of 2022, but only 193 of them had received their first vaccine dose on a week that started in the second half of 2022 (whatdotheyknow.com/request/deaths_in_nims_database#incoming-2653782):
t=read.csv("Covid19VAccineDataForThoseWithADeathRecordv5.csv")
for(i in grep("Date",colnames(t)))t[,i]=as.Date(t[,i],"%d/%m/%Y")
d1=as.Date("2022-7-1");d2=as.Date("2022-12-31")
t=t[t$Dose.Number==1&t$Date.of.Death%in%d1:d2,]
sum(t$Record.Count) # 269247
sum(t$Record.Count[t$Dose.Date%in%d1:d2]) # 193