A mercury film was deposited on an iridium substrate by reduction of a mercury salt. The nonlinear optical response from the mercury film in KF and KPF6 electrolyte solutions was then found to follow the expected behaviour for a pure free electron gas metal. The SH intensity is a parabolic function of the metal surface charge and the minimum of the parabola is very close to the point of zero charge. In the non-adsorbing KF electrolyte solution, the parabolic model is shown to account correctly for the experimental data. The sensitivity of the technique to specific adsorption is also underlined with the use of the weakly adsorbing KPF6 electrolyte solution. Furthermore, the absolute magnitude of the nonlinear reflectance is determined against a quartz reference for various angles of incidence leading to the unambiguous determination of the nonlinear optical parameter a(sigma) for the mercury film electrode as a function of the surface charge. Finally, owing to its long term stability and pure bulk metal response, it is emphasised that mercury film electrodes electroplated on iridium substrates can be used efficiently to perform nonlinear optical experiments on the adsorption of compounds at the mercury I electrolyte interface.