We show that a neutral polymer (PEG) induces a topology transition of the bilayers of an ionic surfactant system (SDS-hexanol-brine), provided that the electrostatic interactions between membranes are screened. Hexanol is used as a cosurfactant in order to get a lamellar or a sponge phase, depending on the cosurfactant/surfactant mass ratio. Using brine as solvent, the addition of polymer triggers a transformation between flat or saddle-like bilayers into vesicles. This modification is not observed in pure water because of the electrostatic repulsion between membranes. The effect can be understood in terms of the modification of the membrane Gaussian modulus due to polymer adsorption and of the entropy gain of the adsorbed polymer when the membrane bends to form a vesicle. © 2009 Springer-Verlag.