https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/deathsbyvaccinationstatusengland
Deaths from all causes.
Blue line is UNVACCINATED
Brown line is VACCINATED
I did look at the downloaded data which ONLY provides detail by vax status and age, NOT by cause of death. It supports the chart but does not allow for any meaningful conclusion to be made regarding whether being vaccinated or unvaccinated contributed to, or prevented deaths. Crunching the numbers, as you advise, doesn't change anything.