The formation and evolution of galaxies with low neutral atomic hydrogen (H I) masses, MHI < 108 h-2 M⊙, are affected by host dark matter halo mass and photoionization feedback from the UV background after the end of reionization. We study how the physical processes governing the formation of galaxies with low HI mass are imprinted on the distribution of neutral hydrogen in the Universe using the hierarchical galaxy formation model, GALFORM. We calculate the effect on the correlation function of changing the HI mass detection threshold at redshifts 0 ≤ z ≤ 0.5. We parametrize the clustering as ξ (r) = (r/r0)-γ and we find that including galaxies with MHI < 108 h-2 M⊙ increases the clustering amplitude r0 and slope γ compared to samples of higher HI masses. This is due to these galaxies with low HI masses typically being hosted by haloes with masses greater than 1012 h-1 M⊙, and is in contrast to optically selected surveys for which the inclusion of faint, blue galaxies lowers the clustering amplitude. We show the HI mass function for different host dark matter halo masses and galaxy types (central or satellite) to interpret the values of r0 and γ of the clustering of HIselected galaxies. We also predict the contribution of low HI mass galaxies to the 21 cm intensity mapping signal. We calculate that a dark matter halo mass resolution better than ~1010 h-1 M⊙ at redshifts higher than 0.5 is required in order to predict converged 21 cm brightness temperature fluctuations.