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Context. The solid-state reaction C + H₂O → H₂CO has recently been studied experimentally and claimed as a new ‘non-energetic’ pathway to complex organic and prebiotic molecules in cold astrophysical environments. Aims. We compared results of astrochemical network modelling with and without the C + H₂O surface reaction. Methods. A typical, generic collapse model in which a dense core forms from initially diffuse conditions was used along with the astrochemical kinetics model MAGICKAL. Results. The inclusion of the reaction does not notably enhance the abundance of formaldehyde itself; however, it significantly enhances the abundance of methanol (formed by the hydrogenation of formaldehyde) on the dust grains at early times, when the high gas-phase abundance of atomic C leads to relatively rapid adsorption onto the grain surfaces. As a result, the gas-phase abundance of methanol is also increased due to chemical desorption, quickly reaching abundances close to ∼10⁻⁹n_H, which decline strongly under late-time, high-density conditions. The reaction also influences the abundances of simple ice species, with the CO₂abundance increased in the earliest, deepest ice layers, while the water-ice abundance is somewhat depressed. The abundances of various complex organic molecules are also affected, with some species becoming more abundant and others less. When gas-phase atomic carbon becomes depleted, the grain-surface chemistry returns to behaviour that would be expected if there had been no new reaction. Conclusions. Our results show that fundamental reactions involving the simplest atomic and molecular species can be of great importance for the evolution of astrochemical reaction networks, thus providing motivation for future experimental and theoretical studies.