We compare the mass and internal distribution of atomic hydrogen (H I) in 2200 present-day central galaxies with Mstar > 1010 M⊙ from the 100 Mpc EAGLE `Reference' simulation to observational data. Atomic hydrogen fractions are corrected for self-shielding using a fitting formula from radiative transfer simulations and for the presence of molecular hydrogen using an empirical or a theoretical prescription from the literature. The resulting neutral hydrogen fractions, M_{H_I+H_2} / M_star, agree with observations to better than 0.1 dex for galaxies with Mstar between 1010 and 1011 M⊙. Our fiducial, empirical H2 model based on gas pressure results in galactic H I mass fractions, M_{H I/ M_star, that agree with observations from the GASS survey to better than 0.3 dex, but the alternative theoretical H2 formula from high-resolution simulations leads to a negative offset in M_{H I}/ M_star of up to 0.5 dex. Visual inspection of mock H I images reveals that most H I discs in simulated H I-rich galaxies are vertically disturbed, plausibly due to recent accretion events. Many galaxies (up to 80 per cent) contain spuriously large H I holes, which are likely formed as a consequence of the feedback implementation in EAGLE. The H I mass-size relation of all simulated galaxies is close to (but 16 per cent steeper than) observed, and when only galaxies without large holes in the H I disc are considered, the agreement becomes excellent (better than 0.1 dex). The presence of large H I holes also makes the radial H I surface density profiles somewhat too low in the centre, at Σ _{H I} > 1 M_{⊙} pc^{-2} (by a factor of ≲ 2 compared to data from the Bluedisk survey). In the outer region (Σ _{H I} < 1 M_{⊙} pc^{-2}), the simulated profiles agree quantitatively with observations. Scaled by H I size, the simulated profiles of H I-rich (M_{H I}> 10^{9.8} M_{⊙}) and control galaxies (10^{9.1} M_{⊙}> M_{H I} > 10^{9.8} M_{⊙}) follow each other closely, as observed.