  Intermediate resolution (R=7000) spectroscopy is presented for 76
photometrically selected very low mass (0.04<M<0.3M_{sun}) candidate members of
the Sigma Orionis cluster. More than two thirds appear to be genuine cluster
members on the basis of Li I absorption, weak Na I features and radial
velocities. 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. Four candidate
binary cluster members are identified. Consideration of sampling and precision
leads us to conclude that either the fraction of very low mass stars and brown
dwarfs in small separation (a<1au) 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, but is significant even when only
Li-rich candidate members 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+/-5 per cent) is similar to that found in stars of
higher mass in the 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 less than 10^{-11} M_sun/yr is
hence less than the age of the Sigma Ori cluster (3 to 7 Myr) for most low-mass
objects (abridged).
