We present an optical to submillimetre multiwavelength study of two very low-luminosity Class I/flat systems, Mayrit 1701117 and Mayrit 1082188, in the σ Orionis cluster. We performed moderate-resolution (R ˜ 1000) optical (˜0.4-0.9 μm) spectroscopy with the Cassegrain Twin Spectrograph (TWIN) spectrograph at the Calar Alto 3.5-m telescope. The spectra for both sources show prominent emission in accretion- and outflow-associated lines. The mean accretion rate measured from multiple line diagnostics is 6.4 × 10-10 M⊙ yr-1 for Mayrit 1701117 and 2.5 × 10-10 M⊙ yr-1 for Mayrit 1082188. The outflow mass-loss rates for the two systems are similar and estimated to be ˜1 × 10-9 M⊙ yr-1. The activity rates are within the range observed for low-mass Class I protostars. We obtained submillimetre continuum observations with the Submillimetre Common-User Bolometer Array (SCUBA-2) bolometer at the James Clerk Maxwell Telescope. Both objects are detected at a ≥5σ level in the SCUBA-2 850-μm band. The bolometric luminosity of the targets as measured from the observed spectral energy distribution over ˜0.8-850 μm is 0.18 ± 0.04 L⊙ for Mayrit 1701117 and 0.16 ± 0.03 L⊙ for Mayrit 1082188 and is in the very low mass range. The total dust+gas mass derived from submillimetre fluxes is ˜36 MJup and ˜22 MJup for Mayrit 1701117 and Mayrit 1082188, respectively. There is the possibility that some of the envelope material might be dissipated by the strong outflows driven by these sources, resulting in a final mass of the system close to or below the substellar limit.