Atmospheric warming is increasing surface melting across the Antarctic Peninsula, with unknown impacts upon glacier dynamics at the ice-bed interface. Using high-resolution satellite-derived ice velocity data, optical satellite imagery and regional climate modelling, we show that drainage of surface meltwater to the bed of outlet glaciers on the Antarctic Peninsula occurs and triggers rapid ice flow accelerations (up to 100% greater than the annual mean). This provides a mechanism for this sector of the Antarctic Ice Sheet to respond rapidly to atmospheric warming. We infer that delivery of water to the bed transiently increases basal water pressure, enhancing basal motion, but efficient evacuation subsequently reduces water pressure causing ice deceleration. Currently, melt events are sporadic, so efficient subglacial drainage cannot be maintained, resulting in multiple short-lived (<6 day) ice flow perturbations. Future increases in meltwater could induce a shift to a glacier dynamic regime characterised by seasonal-scale hydrologically-driven ice flow variations.