ABSTRACT Disc winds are a common feature in accreting astrophysical systems on all scales. In active galactic nuclei (AGNs) and accreting white dwarfs (AWDs), specifically, radiation pressure mediated by spectral lines is a promising mechanism for driving these outflows. Previous hydrodynamical simulations have largely supported this idea, but relied on highly approximate treatments of ionization and radiative transfer. Given the sensitivity of line driving to the ionization state and radiation field in the outflow, here, we present a new method for carrying out 2.5D radiation hydrodynamic simulations that takes full account of the frequency-dependent radiative transfer through the wind, the corresponding ionization state, and the resulting radiative accelerations. Applying our method to AWDs, we find that it is much harder to drive a powerful line-driven outflow when the interaction between matter and radiation is treated self-consistently. This conclusion is robust to changes in the adopted system parameters. The fundamental difficulty is that discs luminous enough to drive such a wind are also hot enough to overionize it. As a result, the mass-loss rates in our simulations are much lower than those found in earlier, more approximate calculations. We also show that the ultraviolet spectra produced by our simulations do not match those observed in AWDs. We conclude that, unless the overionization problem can be mitigated (e.g. by subgrid clumping or a softer-than-expected radiation field), line driving may not be a promising mechanism for powering the outflows from AWDs. These conclusions are likely to have significant implications for disc winds in AGN also.