ABSTRACT Using new Very Large Telescope (VLT)/XShooter spectral observations we analyse the physical properties of five z ∼ 0.3–0.4 confirmed Lyman continuum (LyC) leakers. Strong resonant Mg ii λλ2796, 2803 Å emission lines (I(λλ2796, 2803)/I(Hβ) ≃ 10–38 per cent) and non-resonant Fe ii* λλ2612, 2626 Å emission lines are observed in spectra of five and three galaxies, respectively. We find high electron densities Ne ∼ 400 cm−3, significantly higher than in typical low-z, but comparable to those measured in z ∼ 2–3 star-forming galaxies (SFGs). The galaxies have a mean value of log N/O = –1.16, close to the maximum values found for SFGs in the metallicity range of 12 + log O/H ≃ 7.7–8.1. All 11 low-z LyC emitting galaxies found by Izotov et al., including the ones considered in this study, are characterized by high equivalent width (EW) (Hβ) ∼ 200–400 Å, high ionization parameter (log(U) = –2.5 to –1.7), high average ionizing photon production efficiency ξ = 1025.54 Hz erg−1, and hard ionizing radiation. On the Baldwin–Phillips–Terlevich (BPT) diagram we find the same offset of our leakers from low-z main-sequence SFGs as that for local analogues of Lyman-break galaxies (LBGs) and extreme SFGs at z ∼ 2–3. We confirm the effectiveness of the He i emission lines diagnostics proposed by Izotov et al. in searching for LyC leaker candidates and find that their intensity ratios correspond to those in a median with low neutral hydrogen column density N(H i) = 1017–5 × 1017 cm−2 that permit leakage of LyC radiation, likely due to their density-bounded H ii regions.