Estimating an infectious disease attack rate requires inference on the number of reported symptomatic cases of a disease, the number of unreported symptomatic cases, and the number of asymptomatic infections. Population-level immunity can then be estimated as the attack rate plus the number of vaccine recipients who had not been previously infected; this requires an estimate of the fraction of vaccines that were distributed to seropositive individuals. To estimate attack rates and population immunity in southern New England, we fit a validated dynamic epidemiological model to case, clinical, and death data streams reported by Rhode Island, Massachusetts, and Connecticut for the first 15 months of the COVID-19 pandemic, from March 1 2020 to May 31 2021. This period includes the initial spring 2020 wave, the major winter wave of 2020-2021, and the lagging wave of lineage B.1.1.7(Alpha) infections during March-April 2021. In autumn 2020, SARS-CoV-2 population immunity (equal to the attack rate at that point) in southern New England was still below 15%, setting the stage for a large winter wave. After the roll-out of vaccines in early 2021, population immunity in many states was expected to approach 70% by spring 2021, with more than half of this immune population coming from vaccinations. Our population immunity estimates for May 31 2021 are 73.4% (95% CrI: 72.9% - 74.1%) for Rhode Island, 64.1% (95% CrI: 64.0% - 64.4%) for Connecticut, and 66.3% (95% CrI: 65.9% - 66.9%) for Massachusetts, indicating that >33% of southern Englanders were still susceptible to infection when the Delta variant began spreading in July 2021. Despite high vaccine coverage in these states, population immunity in summer 2021 was lower than planned due to 34% (Rhode Island), 25% (Connecticut), and 28% (Massachusetts) of vaccine distribution going to seropositive individuals. Future emergency-setting vaccination planning will likely have to consider over-vaccination as a strategy to ensure that high levels of population immunity are reached during the course of an ongoing epidemic.