Electrospinning parameters are optimized for the preparation of fibrous membranes of poly(vinylidene fluoride-co-hexafluoropropylene) {P(VdF-HFP)} that consist of layers of uniform fibres of average diameter 1μm. Electrospinning of a 16wt.% solution of the polymer in acetone/N,N-dimethylacetamide (DMAc) (7/3, w/w) at an applied voltage of 18kV results in obtaining membranes with uniform morphology. Polymer electrolytes (PEs) are prepared by activating the membrane with liquid electrolytes. The fully interconnected porous structure of the host polymer membrane enables high electrolyte uptake and ionic conductivities of 10−3 Scm−1 order at 20°C. The PEs have electrochemical stability at potentials higher than 4.5V versus Li/Li+. A PE based on a membrane with 1M LiPF6 in ethylene carbonate (EC)/dimethyl carbonate (DMC), which exhibits a low and stable interfacial resistance on lithium metal, is evaluated for discharge capacity and cycle properties in Li/LiFePO4 cells at room temperature and different current densities. A remarkably good performance with a high initial discharge capacity and low capacity fading on cycling is obtained.