You can't really tell that from this table because vaccinated people may be more likely to get a test. Anyone who thinks the whole thing is a hoax probably won't get a test until they are really sick.
Your table does show that unvaccinated people are much more likely to be hospitalized or to die because of covid.
Your response to the data seems to be evidence of someone trying to bend the data to their previously held ideas.
Your hypothesis to explain the data is that vaccinated people in the UK get themselves tested at a rate twice that of unvaccinated people in an environment where testing is mandatory in many situations, and apparently mandatory in more situations among the unvaccinated.
In addition, in order to get twice the rate of confirmed infections among the vaccinated as the unvaccinated what do you think the "breakthrough" rate has to be?
Wouldn't a simpler explanation be that vaccines distributed in the UK have limited effectiveness after a fairly short period of time and against new COVID strains?