Underground Hydrogen Storage (UHS) has gathered interest over the past decade as an efficient means of storing energy. Although a significant number of research and demonstration projects have sought to understand the associated technical challenges, it is yet to be achieved on commercial scales. We highlight case studies from town gas and blended hydrogen storage focusing on leakage pathways and hydrogen reactivity. Experience from helium storage serves as an analogue for the containment security of hydrogen as the two gases share physiochemical similarities, including small molecular size and high diffusivity. Natural gas storage case studies are also investigated, to highlight well integrity and safety challenges. Technical parameters identified as having adverse effects on storage containment security, efficiency, and hydrogen reactivity were then used to develop high-level and site-specific screening criteria. Thirty-two depleted offshore hydrocarbon reservoirs in the UK Continental Shelf (UKCS) are identified as potential storage formations based on the application of our high-level criteria. The screened fields reflect large hydrogen energy capacities, low cushion gas requirements, and proximity to offshore wind farms, thereby highlighting the widespread geographic availability and potential for efficient UHS in the UKCS. Following the initial screening, we propose that analysis of existing helium concentrations and investigation of local tectonic settings are key site-specific criteria for identifying containment security of depleted fields for stored hydrogen.