Surface‐derived meltwater can access the bed of the Greenland Ice Sheet, causing seasonal velocity variations. The magnitude, timing and net impact on annual average ice flow of these seasonal perturbations depends on the hydraulic efficiency of the subglacial drainage system. We examine the relationships between drainage system efficiency and ice velocity, at three contrasting tidewater glaciers in southwest Greenland during 2014‐2019, using high‐resolution remotely sensed ice velocities, modelled surface melting, subglacial discharge at the terminus and results from buoyant plume modelling. All glaciers underwent a seasonal speed‐up, which usually coincided with surface melt‐onset, and subsequent slow‐down, which usually followed inferred subglacial channelisation. The amplitude and timing of these speed variations differed between glaciers, with the speed‐up being larger and more prolonged at our fastest study glacier. At all glaciers, however, the seasonal variations in ice flow are consistent with inferred changes in hydraulic efficiency of the subglacial drainage system, and qualitatively indicative of a flow regime in which annually‐averaged ice velocity is relatively insensitive to inter‐annual variations in meltwater supply – so‐called ‘ice flow self‐regulation’. These findings suggest that subglacial channel formation may exert a strong control on seasonal ice flow variations, even at fast‐flowing tidewater glaciers.