Background: There is limited information on the inequity of access to vaccination in low-and-middle-income countries during the COVID-19 pandemic. Here, we described the progression of the Brazilian immunisation program for COVID-19, and the association of socioeconomic development with vaccination rates, considering the potential protective effect of primary health care coverage. Methods: We performed an ecological analysis of COVID-19 immunisation data from the Brazilian National Immunization Program from January 17 to August 31, 2021. We analysed the dynamics of vaccine coverage in the adult population of 5,570 Brazilian municipalities. We estimated the association of human development index (HDI) levels (low, medium, and high) with age-sex standardised first dose coverage using a multivariable negative binomial regression model. We evaluated the interaction between the HDI and primary health care coverage. Finally, we compared the adjusted monthly progression of vaccination rates, hospital admission and in-hospital death rates among HDI levels. Findings: From January 17 to August 31, 2021, 202,427,355 COVID-19 vaccine doses were administered in Brazil. By the end of the period, 64·2% of adults had first and 31·4% second doses, with more than 90% of those aged ≥60 years with primary scheme completed. Four distinct vaccine platforms were used in the country, ChAdOx1-S/nCoV-19, Sinovac-CoronaVac, BNT162b2, Ad26.COV2.S, composing 44·8%, 33·2%, 19·6%, and 2·4% of total doses, respectively. First dose coverage differed between municipalities with high, medium, and low HDI (Median [interquartile range] 72 [66, 79], 68 [61, 75] and 63 [55, 70] doses per 100 people, respectively). Municipalities with low (Rate Ratio [RR, 95% confidence interval]: 0·87 [0·85-0·88]) and medium (RR [95% CI]: 0·94 [0·93-0·95]) development were independently associated with lower vaccination rates compared to those with high HDI. Primary health care coverage modified the association of HDI and vaccination rate, improving vaccination rates in those municipalities of low HDI and high primary health care coverage. Low HDI municipalities presented a delayed decrease in adjusted in-hospital death rates by first dose coverage compared to high HDI locations. Interpretation: In Brazil, socioeconomic disparities negatively impacted the first dose vaccination rate. However, the primary health care mitigated these disparities, suggesting that the primary health care coverage guarantees more equitable access to vaccines in vulnerable locations.