Urban public health is one of the most critical yet neglected aspects of urban planning in developing countries such as India. Inequity in access to government healthcare facilities affects the overall urban population and can substantially negatively impact the vulnerable population, who mostly rely on government healthcare services. In this paper, the accessibility measure for healthcare services by public transport is developed using travel time and the number of transit stops (accounting for transit connectivity) for Greater Mumbai. We also identified socially vulnerable wards (administrative units) using a Social Vulnerability Index (SVI), developed based on 16 indicators using Principal Component Analysis (PCA). Developed regression models showed that the proposed accessibility measure explains the coverage and usage of healthcare services better than the traditional accessibility measure, which is based on only aggregate level travel time impedances. South Mumbai has relatively better accessibility for public hospitals and dispensaries, whereas, lower level of accessibility is observed in the eastern part for public healthcare services. Assessment for the spatial inequity based on the Gini index, bivariate Moran's I, and mean access value reveals a higher degree of spatial inequity for accessing government hospitals for the slum population. The study developed a decision framework to suggest effective policy measures, which can be prioritised based on SVI to reduce the disparity in the spatial distribution of accessibility to government healthcare systems for vulnerable groups. Our findings can aid transportation and urban planners, health researchers, and policymakers to improve accessibility in under-served areas and give special attention to the needs of the vulnerable population.