Ionic migration has been proposed as a possible cause of photovoltaic current-voltage hysteresis in hybrid perovskite solar cells. A major objection to this hypothesis is that hysteresis can be reduced by changing the interfacial contact materials; this is unlikely to significantly influence the behaviour of mobile ionic charge within the perovskite phase. Here we show that the primary effects of ionic migration can in fact be observed regardless of whether the contacts were changed to give devices with or without significant hysteresis. Transient optoelectronic measurements combined with device simulations indicate that electric-field screening, consistent with ionic migration, is similar in both high and low hysteresis CH3NH3PbI3 cells. Simulation of the photovoltage and photocurrent transients shows that hysteresis requires the combination of both mobile ionic charge and recombination near the perovskite-contact interfaces. Passivating contact recombination results in higher photogenerated charge concentrations at forward bias which screen the ionic charge, reducing hysteresis.