Context. Carbon monosulphide (CS) is among the most abundant gas-phase S-bearing molecules in cold dark molecular clouds. It is easily observable with several transitions in the millimeter wavelength range, and has been widely used as a tracer of the gas density in the interstellar medium in our Galaxy and external galaxies. However, chemical models fail to account for the observed CS abundances when assuming the cosmic value for the elemental abundance of sulfur. Aims. The CS+O → CO + S reaction has been proposed as a relevant CS destruction mechanism at low temperatures, and could explain the discrepancy between models and observations. Its reaction rate has been experimentally measured at temperatures of 150-400 K, but the extrapolation to lower temperatures is doubtful. Our goal is to calculate the CS+O reaction rate at temperatures <150 K which are prevailing in the interstellar medium. Methods. We performed ab initio calculations to obtain the three lowest potential energy surfaces (PES) of the CS+O system. These PESs are used to study the reaction dynamics, using several methods (classical, quantum, and semiclassical) to eventually calculate the CS + O thermal reaction rates. In order to check the accuracy of our calculations, we compare the results of our theoretical calculations for T ~ 150-400 K with those obtained in the laboratory. Results. Our detailed theoretical study on the CS+O reaction, which is in agreement with the experimental data obtained at 150-400 K, demonstrates the reliability of our approach. After a careful analysis at lower temperatures, we find that the rate constant at 10 K is negligible, below 10-15 cm s-1, which is consistent with the extrapolation of experimental data using the Arrhenius expression. Conclusions. We use the updated chemical network to model the sulfur chemistry in Taurus Molecular Cloud 1 (TMC 1) based on molecular abundances determined from Gas phase Elemental abundances in Molecular CloudS (GEMS) project observations. In our model, we take into account the expected decrease of the cosmic ray ionization rate, ζH2, along the cloud. The abundance of CS is still overestimated when assuming the cosmic value for the sulfur abundance.