Links between urban green infrastructure (UGI) and public health benefits are becoming well established. Despite this, how UGI is distributed varies widely. Although not a universal finding, sectors of society that are disadvantaged often suffer from poor provision, something which might be due to which UGI are examined. We assess the distribution of street trees and public greenspaces (two types of publicly-owned and accessible UGI) across the city of Bradford, UK which is characterised by high levels of inequality and variation in ethno-racial background. We do this through statistical and spatial analyses. Street tree density was distributed unevenly and was highest in neighbourhoods with a high proportion of Asian/Asian British residents and with lower socio-economic status. Conversely, neighbourhoods with better access to public greenspaces were characterised by high income and/or a high proportion of White households. While the quality of public greenspace was spatially clustered, there were only limited spatial associations with ethno-racial group or socio-economic status. Population density was a key determinant of the distribution of UGI, suggesting understanding UGI distributions should also focus on urban form. Nevertheless, within the same city we show that equitable distribution of UGI differs according to the form and characteristics of UGI. To fully realise the public health benefits of UGI, it is necessary to map provision and understand the causal drivers of unequal distributions. This would facilitate interventions that promote equitable distributions of UGI based on the needs of the target populations.