The simplest illustration can be seen from the sero prevalence data from the 19th April '21, when 69.3% of people had Covid antibodies, yet at the same time the greatest number that could have had them from vaccination was 31%. Given that many of those 31% would be people who already had antibodies from exposure before they were vaccinated, it can be seen that at that stage vaccination was already a minor player in delivering antibodies, a significance that has continued to diminish since. About 90% of people currently being vaccinated will already have antibodies.
The most recent data you quote references June 28th - over four weeks ago now. By looking at prior numbers and extending the line, taking into account an expected attenuation; you can arrive at a figure of approximately 95% today. However the recent surge in cases must have accelerated the 'mop-up' element. There's quite a high likelihood the current figure is over 96% now - we can certainly be confident about 95%.
(All data from official sources)