Intermediate resolution ( R \sim 7000 ) spectroscopy is presented for 76 photometrically selected very low mass ( 0.04 < M < 0.3 M _ { \odot } ) candidate members of the young cluster around \sigma Orionis . More than two thirds appear to be genuine cluster members on the basis that they exhibit Li i 6708Å absorption , weak Na i 8183/8195Å features and a radial velocity consistent with the cluster mean . Photometric selection alone therefore appears to be very effective in identifying cluster members in this mass range . Only 6 objects appear to be certain non-members , however a substantial subset of 13 have ambiguous or contradictory indications of membership and lack Li absorption . This together with an observed spread in the equivalent width of the Li absorption feature in the cooler stars of our sample indicates there may be deficiencies in our understanding of the formation of this line in cool , low-gravity objects . Four candidate binary cluster members are identified . Consideration of sampling and radial velocity measurement precision leads us to conclude that either the fraction of very low mass stars and brown dwarfs in small separation ( a < 1 au ) binary systems is larger than in field M-dwarfs , or the distribution of separations is much less skewed towards large separations . This conclusion hinges critically on the correct identification of the small number of binary candidates , although it remains significant even when only the candidate members displaying Li absorption are considered . Broadened H \alpha emission , indicative of circum ( sub ) stellar accretion discs is found in 5 or 6 of the candidate cluster members , 3 of which probably have substellar masses . The fraction of accretors ( 10 \pm 5 per cent ) is similar to that found in stars of higher mass in the \sigma Ori cluster using H \alpha emission as a diagnostic , but much lower than found for very low mass stars and brown dwarfs of younger clusters . The timescale for accretion rates to drop to \la 10 ^ { -11 } M _ { \odot } yr ^ { -1 } is hence less than the age of the \sigma Ori cluster ( 3 to 7 Myr ) for most low-mass objects .