Using the Parkes radio telescope, we study the 21 cm neutral hydrogen (H i) properties of a sample of galaxies with redshifts z < 0.13 extracted from the optical Two-Degree-Field Galaxy Redshift Survey (2dFGRS). Galaxies at 0.04 < z < 0.13 are studied using new Parkes observations of a 42 deg2 field near the South Galactic Pole (SGP). A spectral stacking analysis of the 3277 2dFGRS objects within this field results in a convincing 12σ detection. For the low-redshift sample at 0 < z < 0.04, we use the 15 093 2dFGRS galaxies observed by the H i Parkes All-Sky Survey (HIPASS) and find a 31σ stacked detection. We measure average H i masses of (6.93 ± 0.17) × 109 and (1.48 ± 0.03) × 109 h −2 M for the SGP and HIPASS samples, respectively. Accounting for source confusion and sample bias, we find a cosmic H i mass density of ΩHI = (3.19−0.59 +0.43) × 10−4 h−1 for the SGP sample and (2.82−0.59 +0.30) × 10−4 h−1 for the HIPASS sample. This suggests no (12 ± 23 per cent) evolution in the cosmic H i density over the last ∼1 h −1 Gyr. Due to the very large effective volumes, cosmic variance in our determination of ΩHI is considerably lower than previous estimates. Our stacking analysis reproduces and quantifies the expected trends in the H i mass and mass-to-light ratio of galaxies with redshift, luminosity and colour.