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The spatial distribution of metals reflects, and can be used to constrain, the processes of chemical enrichment and mixing. Using PHANGS-MUSE optical integral field spectroscopy, we measure the gas phase oxygen abundances (metallicities) across 7,138 HII regions in a sample of eight nearby disc galaxies. In Paper I (Kreckel et al. 2019) we measure and report linear radial gradients in the metallicities of each galaxy, and qualitatively searched for azimuthal abundance variations. Here, we examine the two-dimensional variation in abundances once the radial gradient is subtracted, Delta(O/H), in order to quantify the homogeneity of the metal distribution and to measure the mixing scale over which HII region metallicities are correlated. We observe low (0.03--0.05 dex) scatter in Delta(O/H) globally in all galaxies, with significantly lower (0.02--0.03 dex) scatter on small (<600 pc) spatial scales. This is consistent with the measurement uncertainties, and implies the two-dimensional metallicity distribution is highly correlated on scales of <600 pc. We compute the two point correlation function for metals in the disc in order to quantify the scale lengths associated with the observed homogeneity. This mixing scale is observed to correlate better with the local gas velocity dispersion (of both cold and ionized gas) than with the star formation rate. Selecting only HII regions with enhanced abundances relative to a linear radial gradient, we do not observe increased homogeneity on small scales. This suggests that the observed homogeneity is driven by the mixing introducing material from large scales rather than by pollution from recent and on-going star formation.