In this paper, a model-based predictive control method is proposed for utilization of flexible resources such as battery energy storage systems and heating systems effectively to provide demand response in low-voltage distribution networks with solar photovoltaic. The contributions of this paper are twofold. First, a linear power flow method based on relaxation of branch power losses applicable to radial distribution networks is proposed and formulated. Second, a flexible resources controller that solves a multi-objective linear optimization problem in receding-horizon fashion is formulated taking into account system states, forecasts of generation, and loads. Using the proposed control algorithm, flexibility from network resources can be utilized for low-voltage network management with assurance of quality of service to the customers. Simulations are conducted for summer and winter cases on a simplified Danish low-voltage network using Matlab/Simulink to study the performance of the proposed control method. Compared to the methods in state of the art, the proposed linear power flow method is proven to be accurate for the calculation of network power flows. Simulation results also show that proposed flexible resources controller can meet the network control objectives while satisfying the network constraints and operation limits of the flexible resources.