A binned Dalitz plot analysis of B +/- a D K +/- decays, with D a K S 0 pi + pi - and D a K S 0 K + K - , is performed to measure the CP-violating observables x +/- and y +/- which are sensitive to the CKM angle gamma. 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) X 10 - 2 , y - = (2.7 +/- 5.2 +/- 0.8 +/- 2.3) X 10 - 2 , x + = (- 10.3 +/- 4.5 +/- 1.8 +/- 1.4) X 10 - 2 and y + = (- 0.9 +/- 3.7 +/- 0.8 +/- 3.0) X 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 gamma = (44 - 38 + 43) degree , with a second solution at gamma a gamma + 180 degree , and r B = 0.07 +/- 0.04 , where r B is the ratio between the suppressed and favoured B decay amplitudes.