ABSTRACT We predict late-time optical/UV emission from tidal disruption events (TDEs) from our slim accretion disc model (Wen et al. 2020) and explore the impact of the black hole mass M•, black hole spin a•, and accretion disc size. We use these synthetic spectra to successfully fit the multiband Swift observations of ASASSN-14li at >350 d, setting only the host galaxy extinction and outer disc radius as free parameters and employing the M•, a•, disc inclination, and disc accretion rates derived from fitting 10 epochs of ASASSN-14li’s X-ray spectra with the slim disc. To address the nature of the early-time optical/UV emission, we consider two models: shock dissipation and reprocessing. We find that (1) the predicted late-time optical/UV colour (e.g. u − w2) is insensitive to black hole and disc parameters unless the disc spreads quickly; (2) a starburst galaxy extinction model is required to fit the data, consistent with ASASSN-14li’s post-starburst host; (3) surprisingly, the outer disc radius is ≈2 × the tidal radius and ∼constant at late times, showing that viscous spreading is slow or non-existent; (4) the shock model can be self-consistent if M• ≲ 106.75 M⊙, i.e. on the low end of ASASSN-14li’s M• range (106.5–7.1 M⊙; 1σ CL); larger black hole masses require disruption of an unrealistically massive progenitor star; (5) the gas mass needed for reprocessing, whether by a quasi-static or an outflowing layer, can be <0.5 M⊙, consistent with a (plausible) disruption of a solar-mass star.