Unreported partially/fully closed valves or other type of pipe blockages in water distribution networks result in unexpected energy losses within the systems, which we also refer to as faults. We investigate the problem of detection and localization of such faults. We propose a novel optimization-based method, which relies on the solution of a non-linear inverse problem with l1 regularization. We develop a sequential convex optimization algorithm to solve the resulting non-smooth non-convex optimization problem. The proposed algorithm enables the use of non-smooth terms within the problem formulation, and exploits the sparse structure inherent in water network models. The performance of the developed method is numerically evaluated to detect and localize blockages in a large water distribution network using both simulated and experimental data. In all experiments, the sequential convex optimization algorithm converged in less than three seconds, suggesting that the proposed fault detection and localization method is suitable for near real-time implementation. Furthermore, we experimentally validate the developed method for near real-time fault diagnosis in a large operational water network from the UK. The method is shown to successfully detect and localize blockages, with real system modelling uncertainties.