Emphasis added.
Except that the data is from Feb 1, 2021 - Sep 12, 2021. The 75% vaccination rate is
current, but it's not reflective of the vaccination rate for that time period. They didn't even reach 10% fully vaxxed until April 4. Most people were getting their first shots. Even in March, fully vaxxed rates were very low. They didn't even get to 50% getting 2 shots until June 4, 2020. For more than half of the time period of the statistics, fully vaxxed was < 50%.
While i agree that vaccination rates definitely play into the numbers of vaccinated/unvaccinated outcomes, the numbers you're suggesting aren't applicable to the data being discussed. If anything, there are more unvaccinated people in the UK in the time period discussed. Of course, it's likely more complex than that, as older age groups a) reached a higher vaccination status sooner than the general population and b) older people are also more highly represented in deaths and c) that data is specific to the delta variant, which was more prevalent later, so while the general population may have been less than 50% vaccinated in the time period in which the statistics refer, it's difficult to draw firm conclusions based on the data as presented. A much more granular assessment of data would be needed.
As far as his 1779 number vs 1613, i would agree that the 1613 (having received 2 doses) is more applicable. I believe the 1779 number is reflective of all people having received at least 1 dose. (1613+149+17)
Vaccinations in the UK | Coronavirus in the UK (data.gov.uk)