In this work we report a novel liquid-acid electrochemical cell containing Gortex-based gas diffusion electrodes, layered with suitable catalysts and current collectors, that is capable of sustainably extractin g pure hydrogen from methane mixtures containing as little as 5% hydrogen. The origin of its efficiency appears to derive from the solid-liquid interface between the solid Gortex electrodes and the liquid electrolyte, as well as the high proton conductivity of the electrolyte. This interface and electrolyte exhibit an efficiency for reaction that greatly exceeds that achieved by the comparable solid-solid interface and proton conductor in Proton Exchange Membrane Fuel Cell (PEMFC) technology. We report hydrogen yields and recovery by the cell from a range of methane-hydrogen mixtures. Electrochemical impedance spectroscopy has been used to characterise the cell and to illuminate the system limitations.