We present high- and medium-resolution spectroscopic observations of the cataclysmic variable BF Eridani (BF Eri) during its low and bright states. The orbital period of this system was found to be 0.270881(3) d. The secondary star is clearly visible in the spectra through the absorption lines of the neutral metals Mg i, Fe i and Ca i. Its spectral type was found to be K3±0.5. A radial velocity study of the secondary yielded a semi-amplitude of K2= 182.5 ± 0.9 km s−1. The radial velocity semi-amplitude of the white dwarf was found to be K1= 74 ± 3 km s−1 from the motion of the wings of the Hα and Hβ emission lines. From these parameters, we have obtained that the secondary in BF Eri is an evolved star with a mass of 0.50–0.59 M⊙, whose size is about 30 per cent larger than a zero-age main-sequence single star of the same mass. We also show that BF Eri contains a massive white dwarf (M1≥ 1.2 M⊙), which allows us to consider the system as a Type Ia supernova progenitor. BF Eri also shows a high γ-velocity (γ=−94 km s−1) and substantial proper motion. With our estimation of the distance to the system (d≈ 700 ± 200 pc), this corresponds to a space velocity of ∼350 km s−1 with respect to the dynamical local standard of rest. The cumulative effect of repeated nova eruptions with asymmetric envelope ejection might explain the high space velocity of the system. We analyse the outburst behaviour of BF Eri and question the current classification of the system as a dwarf nova. We propose that BF Eri might be an old nova exhibiting ‘stunted’ outbursts.