Direct collapse black holes (DCBHs) formed from the collapse of atomically cooled primordial gas in the early Universe are strong candidates for the seeds of supermassive BHs. DCBHs are thought to form in atomic cooling haloes in the presence of a strong molecule-dissociating, Lyman–Werner (LW) radiation field. Given that star-forming galaxies are likely to be the source of the LW radiation in this scenario, ionizing radiation from these galaxies may accompany the LW radiation. We present cosmological simulations resolving the collapse of primordial gas into an atomic cooling halo, including the effects of both LW and ionizing radiation. We find that in cases where the gas is not self-shielded from the ionizing radiation, the collapse can be delayed by ∼25 Myr. When the ionized gas does collapse, the free electrons that are present catalyse H2 formation. In turn, H2 cooling becomes efficient in the centre of the halo, and DCBH formation is prevented. We emphasize, however, that in many cases the gas collapsing into atomic cooling haloes at high redshift is self-shielding to ionizing radiation. Therefore, it is only in a fraction of such haloes in which DCBH formation is prevented due to reionization.