Being able to control, safely and accurately, the voltage state of the nodes in distribution networks, subject to given power loads and injections, is of key importance in handling network management and planning problems in the context of an ever increasing role of renewable production facilities and of anticipated growth in EV recharging requirements. We investigate here a new approach to the so-called Load Flow problem in distribution networks (also applicable to mesh networks), based on a 2-Step procedure, and featuring several original capabilities, in particular: for moderately loaded networks, the efficient determination of the high-voltage solution with high accuracy; for highly loaded networks (when the Load Flow problem may not have a solution), the automatic detection of situations of possible overload in the network under consideration. Computational experiments illustrate the accuracy of the solutions produced by the new 2-Step Load Flow algorithm, In addition, a full case study involving LV distribution networks with PV injections and EV recharging illustrate a possible use of the proposed method with respect to practical applications.