In this study, the leaching behaviour of aluminium from waste pharmaceutical blister packages (WPBs) is investigated in sulphuric acid media to build future strategies for aluminium recycling from this non-recycled waste fraction. The results suggest that in hydrometallurgical recycling, passivation of aluminium during leaching can be mitigated in dilute sulphuric acid solutions (0.25 M), at high temperatures (60–80 °C) and specifically with H2O2 addition. With this system, 100% extraction was achieved within five hours under optimized conditions (H2SO4 = 0.25 M, T = 80 °C, H2O2 = 1.25 vol.%). The leaching mechanism is suggested to be based on electrochemical dissolution of metallic aluminium oxidized by H+ or H2O2, followed by fast passivation by Al2O3 and consequent chemical dissolution of Al2O3 at slower kinetics. The calculated activation energy (~69 kJ/mol) suggests that the leaching reaction is controlled by the chemical or electrochemical reaction step rather than diffusion. By WPB leaching, an aluminium sulphate solution could be obtained, suitable for further aluminium sulphate crystallization. This may provide a potential route for the valorisation of aluminium from a currently overlooked waste fraction of pharmaceutical blister packages.