While public green spaces (PGS) are opined to be central in the pandemic recovery, higher accessibility to PGS also mean a higher risk of infection spread from the raised possibility of people encountering each other. This study explores the distributive effects of accessibility of PGS on the COVID-19 cases distribution using a geo-spatially varying network-based risk model at the borough level in London. The coupled effect of social deprivation with accessibility of the PGS was used as an adjustment factor to identify vulnerability. Results indicate that highly connected green spaces with high choice measure were associated with high risk of infection transmission. Socially deprived areas demonstrated higher possibility of infection spread even with moderate connectivity of the PGS. The study demonstrated that only applying a uniform social distancing measure without characterising the infrastructure and social conditions may lead to higher infection transmission.