Underground hydrogen storage (UHS) in depleted hydrocarbon reservoirs and other porous formations such as aquifers is increasingly considered a key large-scale energy buffer for supporting intermittent renewable energy systems. Reliable prediction of hydrogen injectivity, migration, trapping, and recovery efficiency requires robust multiphase flow characterisation, particularly H₂ brine relative permeability. However, hydrogen's low density, high diffusivity, and distinct interfacial properties introduce displacement behaviours that differ fundamentally from those of CO₂ or N₂ based analogues. Experimental datasets for H₂ brine systems, especially in tight sandstones, remain scarce due to operational complexity, hydrogen safety constraints, and measurement uncertainties under low permeability conditions. This study presents primary drainage H₂ brine relative permeability measurements on tight sandstone core plugs spanning a permeability range representative of aquifers originated from depleted gas reservoir intervals considered for UHS. Unsteady state core flooding experiments were conducted in a laboratory approved for hydrogen use equipped with detection, ventilation, and safety control systems, with relative permeability curves derived from measured flow rates and brine production using history matching. The resulting functions exhibit pronounced permeability dependence and systematic differences relative to published CO₂-brine and N₂-brine analogue datasets attributable to hydrogen's distinct fluid properties. These findings demonstrate that directly transferring analogue gas brine relative permeability data to UHS simulations may lead to significant predictive errors in injectivity, pressure evolution, and working gas capacity, underscoring the necessity of fluid and permeability specific parameterisation for reliable UHS performance modelling.