Bayesian modeling of England's 2021 vaccination rollout across 221 local authorities reveals that first COVID vaccine doses reduced population-level transmission by 45.4%, while third doses restored effectiveness to 66.3%. The analysis integrated high-resolution vaccination data with regional transmission patterns, finding that second doses provided negligible additional transmission-blocking benefits beyond the first shot. This population-scale evidence validates smaller household studies and supports the UK's controversial "first-doses-first" strategy that prioritized broader initial coverage over completing two-dose regimens quickly. The findings address a critical gap in vaccine science, as previous transmission studies relied on limited household cohorts that couldn't capture broader ecological impacts on epidemic growth. Notably, socioeconomic deprivation showed no significant correlation with transmission patterns during the rollout period, contrary to expectations. As a preprint awaiting peer review, these results require validation, but they represent the first robust population-level evidence that vaccination substantially reduces SARS-CoV-2's reproduction number. The modeling framework could prove valuable for assessing transmission impacts of vaccines against future respiratory threats, including emerging concerns like H5N1 avian influenza.