Graphene-covering is a promising approach for achieving an acid-stable, non-noble-metal-catalysed hydrogen evolution reaction (HER). Optimization of the number of graphene-covering layers and the density of defects generated by chemical doping is crucial for achieving a balance between corrosion resistance and catalytic activity. Here, we investigate the influence of charge transfer and proton penetration through the graphene layers on the HER mechanisms of the non-noble metals Ni and Cu in an acidic electrolyte. We find that increasing the number of graphene-covering layers significantly alters the HER performances of Ni and Cu. The proton penetration explored through electrochemical experiments and simulations reveals that the HER activity of the graphene-covered catalysts is governed by the degree of proton penetration, as determined by the number of graphene-covering layers.