Hydrogen is seen as a key energy vector in future energy systems due to its ability to be stored in large volumes for long periods, providing energy flexibility and security. Despite the importance of storage in hydrogen's potential role in a zero-carbon energy system, many techno-economic analyses fail to adequately model different storage methods in hydrogen supply chains, often ignoring storage requirements altogether. Therefore, this paper uses a data-driven techno-economic analysis (TEA) tool to examine the effect of storage size and cost on three different 2030 hydrogen supply chain scenarios: wind-based, solar-based, and mixed-source grid electrolysis. For varying storage sizes and specific capital costs, the overall levelised cost of hydrogen (LCOH), including production, storage, and delivery to a constant demand, varies significantly. The LCOH ranges from €3.90–12.40/kgH2, €5.50–12.75/kgH2, and €2.80–15.65/kgH2 for the wind-based, solar-based, and mixed-source grid scenarios respectively, with lower values for scenarios with low-cost storage. This highlights the critical role of low-cost hydrogen storage in realising the energy flexibility and security electrolytic hydrogen can provide.