A binned Dalitz plot analysis of B±→DK± decays, with D→K0Sπ+π− and D→K0SK+K−, is performed to measure the CP-violating observables x± and y± which are sensitive to the CKM angle γ. The analysis exploits 1.0 fb−1 of data collected by the LHCb experiment. The study makes no model-based assumption on the variation of the strong phase of the D decay amplitude over the Dalitz plot, but uses measurements of this quantity from CLEO-c as input. The values of the parameters are found to be x−=(0.0±4.3±1.5±0.6)×10−2, y−=(2.7±5.2±0.8±2.3)×10−2, x+=(−10.3±4.5±1.8±1.4)×10−2 and y+=(−0.9±3.7±0.8±3.0)×10−2. The first, second, and third uncertainties are the statistical, the experimental systematic, and the error associated with the precision of the strong-phase parameters measured at CLEO-c, respectively. These results correspond to γ=(44+43−38)∘, with a second solution at γ→γ+180∘, and rB=0.07±0.04, where rB is the ratio between the suppressed and favoured B decay amplitudes.