I'm not saying it's due to vaccinations, I'm saying it's what you would expect given our pace of vaccinations. All we have are correlations.
The reason I say this is that we have a relatively small population of unvaccinated people, and so with the high R0 of Delta, you'd expect it to rip through these unvaccinated pockets quickly and burn out, which is what we're seeing.
I'd expect a few more Delta mini-waves similar to this in the coming months.
You're right though that the numbers somewhat suggest that we're managing to beat the Delta variant. Is it due to vaccinations? The vaccination rate has been slowing for months now, yet the UK still had that spike. The difference in people that decided to get vaccinated between early June (start of positive cases spike) and July 21st (when the decrease set in) is 9%. (from 59% to 68%). It doesn't seem to me that a few percent more vaccinations explains everything. A percentage in the upper 60s, for first vaccinations no less (not even a full vaccination), should not be enough to beat Delta from what I heard about the R0.
(Data source is the same OWID link, you can configure it to show vaccination data.)