The subglacial hydrological system critically controls ice motion at the margins of the Greenland Ice Sheet. However, over multi-annual timescales, the net impact of hydro-dynamic coupling on ice motion remains poorly understood. Here, we present annual ice velocities from 1992-2019 across a ~10,600 km2 land-terminating area of southwest Greenland. From the early-2000s through to ~2012, we observe a slowdown in ice motion in response to increased surface melt, consistent with previous research. From 2013 to 2019 however, we observe an acceleration in ice motion coincident with atmospheric cooling and a ~15% reduction in mean surface melt production relative to 2003-2012. We find that ice velocity speed-up is greater in marginal areas, and is strongly correlated with ice thickness. We hypothesise that under thinner ice, increases in basal water pressure offset a larger proportion of the ice overburden pressure, leading to reduced effective pressure and thus greater acceleration when compared to thicker ice further inland. Our findings indicate that hydro-dynamic coupling provides the major control on changes in ice motion across the ablation zone of land terminating margins of the Greenland Ice Sheet over multi-annual timescales.