Because of the intense brightness of the OB-type multiple star system σ Ori, the low-mass stellar and substellar populations close to the centre of the very young σ Orionis cluster is poorly know. I present an IJHK_s survey in the cluster centre, able to detect from the massive early-type stars down to cluster members below the deuterium burning mass limit. The near-infrared and optical data have been complemented with X-ray imaging. Ten objects have been found for the first time to display high-energy emission. Previously known stars with clear spectroscopic youth indicators and/or X-ray emission define a clear sequence in the I vs. I-K_s diagram. I have found six new candidate cluster members that follow this sequence. One of them, in the magnitude interval of the brown dwarfs in the cluster, displays X-ray emission and a very red J-K_s colour, indicative of a disc. Other three low-mass stars have excesses in the K_s band as well. The frequency of X-ray emitters in the area is 80±20 %. The spatial density of stars is very high, of up to 1.6±0.1 arcmin-2. There is no indication of lower abundance of substellar objects in the cluster centre. Finally, I also report two cluster stars with X-ray emission located at only 8000-11000 AU to σ Ori AB, two sources with peculiar colours and an object with X-ray emission and near-infrared magnitudes similar to those of previously-known substellar objects in the cluster.