Gyrokinetic codes are used to simulate transport in tokamak plasmas. In these codes, the distribution functions evolve self consistently with an electromagnetic field. To compute the temporal evolution of the electrostatic potential, a quasi-neutrality equation is solved. In some gyrokinetic codes, the quasi-neutrality solver assumes that the background densities and temperatures are constant in time and on flux surfaces. This assumption, which implicitly uses the so-called δF approach, can break up, in particular at the edge of the plasma which can display large and time evolving poloidal asymmetries.In this paper, a numerical solver of the quasi-neutrality equation accounting for time evolving poloidal asymmetries is presented. This solver is compatible with all electron models (adiabatic, kinetic or hybrid) and written for the long wavelength or the Padé approximations for the polarisation term. The impact of such an improvement is carefully reported on different types of simulations, illustrating when the δF approach forquasi-neutrality is valid and when it fails. A procedure to limit the numerical cost of updating the background profiles in the quasi-neutrality solver is also presented.