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This research studies the social and spatial inequalities of contemporary food deserts in England and Wales. Two indices of the Store Food Desert Index and Online Food Desert Index are measured to examine store access and online access to food at the Lower Layer Super Output Areas geographical level. A detailed analysis is conducted to (i) identify "priority areas" where there is relatively lower store access and online access to food, (ii) synthesize population to understand the characteristics of "at-risk communities" that are disproportionately affected by food deserts, and (iii) examine the association between self-reported health conditions and a compound of store and online access to food. Three insights are provided. First, there is a clear urban-rural divide in which urban areas generally benefit from better provision of both store and online access to food. Second, about 23% of the population (13.8 million people) live in priority areas with limited access to both physical stores and online groceries. Within this group, 0.06% (8000 individuals) do not have cars, 2.17% (300,000 individuals) are Black, and 14.5% (2 million individuals) reside in deprived neighborhoods. This is an alarming picture. Third, people residing in areas with high store and online access to food reported better health conditions, and online access is as effective as store access in improving health conditions. The findings highlight the potential of combining online and store access to bridge geographical and economic gaps, thereby providing healthier food options to those in food deserts. • 13.8 million people in the UK have limited access to store and online groceries. • There is a clear urban-rural divide in both store and online access to food. • Deprived households are disproportionately affected by access to food. • People with access to store and online groceries reported better health conditions. • Online access is as practical as store access pertaining to health conditions. [ABSTRACT FROM AUTHOR]