Sediment supply is a fundamental control on the stratigraphic record. However, a key question is the extent to which climate affects sediment fluxes in time and space. To address this question, estimates of sediment fluxes can be compared with measured sediment volumes within a closed basin with well-constrained tectonic boundary conditions and well-documented climate variability. The Corinth rift, central Greece, is one of the most actively extending basins on Earth, with modern day GPS extension rates of up to 15 mm/yr. The Gulf of Corinth forms a closed system and since ~600 ka the gulf has fluctuated between being marine and a lake. We have estimated suspended sediment fluxes for rivers draining into the Gulf of Corinth using the empirically-derived BQART method over the last interglacial-glacial-interglacial cycle (0-130 kyrs). Modern temperature and precipitation datasets, LGM reconstructions and palaeo climate proxy insights were used to constrain model inputs. Simultaneously, we exploited high-resolution 2D seismic surveys to interpret three seismic units from 130 ka to present and we used this data to derive an independent time series of basin sedimentary volumes to compare with our sediment input flux estimates. Our results predict total Holocene sediment fluxes into the Gulf of Corinth of between 19.2 km3 and 23.4 km3 with a preferred estimate of 21.3 km3. This value is a factor of 1.6 less than the measured Holocene sediment volume in the central depocentres, even without taking lithological factors into account, suggesting that the BQART method provides plausible estimates. Sediment fluxes vary spatially around the Gulf, and we use them to derive minimum catchment-averaged denudation rates of 0.18 to 0.55 mm/yr. Significantly, our time series of basin sedimentary volumes demonstrate a clear reduction in sediment accumulation rates during the last glacial period compared to the current interglacial. This implies that Holocene sediment fluxes must have increased relative to late Pleistocene times. Furthermore, BQART-derived sediment flux predictions indicate a 28% reduction in supply during the last glacial period compared to the Holocene, whereas seismic sediment accumulation rate estimates indicate a similar magnitude of reduction (32%). At the Last Glacial Maximum mean annual temperatures in the region were lower by 5 degrees, but mean annual precipitation rates were broadly similar. We hypothesise that although weathering rates might be greater under glacial conditions, warmer interglacial temperatures may be more conducive to generating larger storms, which do more geomorphic work, driving greater sediment fluxes. Our results demonstrate that sediment export to the basin is sensitive to glacial-interglacial cycles and we explore the potential mechanisms behind this sensitivity.