Idealized laboratory experiments have been conducted in a two-layer stratified fluid to investigate the leading-order dynamics that control submarine melting and meltwater export near a vertical ice-ocean interface as a function of subglacial discharge. In summer, the discharge of surface runoff at the base of a glacier (subglacial discharge) generates strong buoyant plumes that rise along the glacier front entraining ambient water along the way. The entrainment enhances the heat transport toward the glacier front and hence the submarine melt rate increases with the subglacial discharge rate. In the laboratory, the effect of subglacial discharge is simulated by introducing freshwater at freezing temperature from a point source at the base ofan ice block representing the glacier. The circulation pattern observed both with and without subglacial discharge resembles those observed in previous observational and numerical studies. Buoyant plumes rise vertically until they find either their neutrally buoyant level or the free surface. Hence, the meltwater can deposit within the interior of the water column and not entirely at the free surface, as confirmed by field observations. The heat budget in the tank, calculated following a new framework, gives estimates of submarine melt rate that increase with the subglacial discharge and are in agreement with the directly measured submarine melting. This laboratory study provides the first direct measurements of submarine melt rates for different subglacial discharges, and the results are consistent with the predictions of previous theoretical and numerical studies.