Look at Table 11 in the attached link. If 100 percent is vaccinated it is impossible that there would be any unvaccinated in the hospital with anything. They don’t exist anymore. Comparing the raw number of vaccinated and unvaccinated in the hospital is ridiculous. In table 11 is shows the rate of hospitalization is about 5 times higher in the unvaccinated group.
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/1039677/Vaccine_surveillance_report_-_week_49.pdf
Average COVID deaths in the UK are 122 per day. In the US it is 1,200 per day. Does that mean they are doing 10 times better at reducing Covid? No, because there are 330mm Americans and only 80 mm Britons. Adjusted for population their death rate is about half of ours. So they are doing twice as well, not 10 times as well. Maybe its because they don’t read posts from “Ransomenote” and “Dailyexpose.uk” which frankly are vomit-inducing garbage.
https://www.worldsometers.info/coronavirus/country/uk/
I realize you want to argue some betterment with the total population thing but the two sentences I gave you from the OP are pretty concise and they are solely between vaccinated and unvaccinated and the experienced hospitalizations, the rate comparisons show HIGHER hospitalizations with the vaccinated, period.
There’s no guessing about the total immunization rate for the entire population and all that. Further, if one were to argue on that basis, I’d argue back that the US has no way of knowing because they don’t even immunize illegals (can’t) and many other groups like the USPS, and other privileged agencies have been given a political pass. I suspect that the UK has a similar problem.