Here we report the results of an experimental and theoretical study of the gas-phase reactions between O(1D) and H2O and O(1D) and D2O at room temperature and below. On the experimental side, the kinetics of these reactions have been investigated over the 50-127 K range using a continuous flow Laval nozzle apparatus, coupled with pulsed laser photolysis and pulsed laser induced fluorescence for the production and detection of O(1D) atoms respectively. Experiments were also performed at 296 K in the absence of a Laval nozzle. On the theoretical side, the existing full-dimensional ground X 1A potential energy surface for the H2O2 system involved in this process has been reinvestigated and enhanced to provide a better description of the barrierless H-atom abstraction pathway. Based on this enhanced potential energy surface, quasiclassical trajectory calculations and ring polymer molecular dynamics simulations have been performed to obtain low temperature rate constants. The measured and calculated rate constants display similar behaviour above 100 K, showing little or no variation as a function of temperature. Below 100 K, the experimental rate constants increase dramatically, in contrast to the essentially temperature independent theoretical values. The possible origins of the divergence between experiment and theory at low temperatures are discussed.