The number density of small dark matter (DM) haloes hosting faint high-redshift galaxies is sensitive to the DM free-streaming properties. However, constraining these DM properties is complicated by degeneracies with the uncertain baryonic physics governing star formation. In this work, we use a flexible astrophysical model and a Bayesian inference framework to analyse ultraviolet (UV) luminosity functions (LFs) at z = 6–8. We vary the complexity of the astrophysical galaxy model (single versus double power law for the stellar – halo mass relation) as well as the matter power spectrum [cold DM versus thermal relic warm DM (WDM)], comparing their Bayesian evidences. Adopting a conservatively wide prior range for the WDM particle mass, we show that the UV LFs at z = 6–8 only weakly favour cold DM over WDM. We find that particle masses of ≲ 2 keV are rejected at a 95 per cent credible level in all models that have a WDM-like power spectrum cutoff. This bound should increase to ∼2.5 keV with the James Webb Space Telescope (JWST).