We present deep kiloparsec- and parsec-scale neutral atomic hydrogen (H I) absorption observations of a very young radio source (≤5000 years), 4C 31.04, using the Westerbork Synthesis Radio Telescope (WSRT) and the Global Very Long Baseline Interferometry (VLBI) array. Using z = 0.0598, derived from molecular gas observations, we detect, at both kpc and pc scales, a broad absorption feature (FWZI = 360 km s−1) centred at the systemic velocity, and narrow absorption (FWZI = 6.6 km s−1) redshifted by 220 km s−1, both previously observed. Additionally, we detect a new blueshifted, broad, shallow absorption wing. At pc scales, the broad absorption at the systemic velocity is detected across the entire radio source while the shallow wing is only seen against part of the eastern lobe. The gas has higher H I column density along the eastern lobe than along the western one. The velocity dispersion of the gas is high (≥40 km s−1) along the entire radio continuum, and is highest (≥60 km s−1) in the region including the outflow and the radio hot spot. While we detect a velocity gradient along the western lobe and parts of the eastern lobe at PA ∼ 5° −10°, most of the gas along the rest of the eastern lobe exhibits no signs of rotation. Earlier optical spectroscopy suggests that the optical AGN is very weak. We therefore conclude that the radio lobes of 4C 31.04 are expanding into a circumnuclear disc, partially disrupting it and making the gas highly turbulent. The distribution of gas is predominantly smooth at the spatial resolution of ∼4 pc studied here. However, clumps of gas are also present, particularly along the eastern lobe. This lobe appears to be strongly interacting with the clouds and driving an outflow ∼35 pc from the radio core, with a mass-outflow rate of 0.3 ≤ Ṁ ≤ 1.4 M⊙ year−1. It is likely that this interaction has caused the eastern lobe to be rebrightened, giving the source an asymmetric morphology. We compare our observations with the predictions of a recent analytical model regarding the survival of atomic gas clouds in radio-jet-driven outflows and find that the existence of a subkpc-scale outflow in this case could imply inefficient mixing of the cold gas with the hot medium and high gas density, leading to very short cooling times. Overall, our study provides further evidence of the strong impact of radio jets on the cold interstellar medium (ISM) in the early stages of their evolution and supports the predictions of numerical simulations regarding jet–ISM interactions and the nature of the circumnuclear gas into which the jets expand.