Theory predicts that cosmological gas accretion plays a fundamental role fuelling star formation in galaxies. However, a detailed description of the accretion process to be used when interpreting observations is still lacking. Using the state-of-the-art cosmological hydrodynamical simulation EAGLE, we work out the chemical inhomogeneities arising in the disc of galaxies due to the randomness of the accretion process. In low-mass systems and outskirts of massive galaxies, low metallicity regions are associated with enhanced star-formation, a trend that reverses in the centres of massive galaxies. These predictions agree with the relation between surface density of star formation rate and metallicity observed in the local spiral galaxies from the MaNGA survey. Then, we analyse the origin of the gas that produce stars at two key epochs, z ≃ 0 and z ≃ 2. The main contribution comes from gas already in the galaxy about 1 Gyr before stars are formed, with a share from external gas that is larger at high redshift. The accreted gas may come from major and minor mergers, but also as gravitationally unbound gas and from mergers with dark galaxies (i.e. haloes where more than 95 per cent of the baryon mass is in gas). We give the relative contribution of these sources of gas as a function of stellar mass (8 ≤ log [M⋆/M⊙] ≤ 11). Even at z = 0, some low-mass galaxies form a significant fraction of their total stellar mass during the last Gyr from mergers with dark galaxies.