Context. The Vela Molecular Ridge is one of the nearest (700 pc) giant molecular cloud (GMC) complexes hosting intermediate-mass (up to early B, late O stars) star formation, and is located in the outer Galaxy, inside the Galactic plane. Vela C is one of the GMCs making up the Vela Molecular Ridge, and exhibits both sub-regions of robust and sub-regions of more quiescent star formation activity, with both low- and intermediate(high)-mass star formation in progress. Aims. We aim to study the individual and global properties of dense dust cores in Vela C, and aim to search for spatial variations in these properties which could be related to different environmental properties and/or evolutionary stages in the various sub-regions of Vela C. Methods. We mapped the submillimetre (345 GHz) emission from vela C with LABOCA (beam size ~19′′2, spatial resolution ~0.07 pc at 700 pc) at the APEX telescope. We used the clump-finding algorithm CuTEx to identify the compact submillimetre sources. We also used SIMBA (250 GHz) observations, and Herschel and WISE ancillary data. The association with WISE red sources allowed the protostellar and starless cores to be separated, whereas the Herschel dataset allowed the dust temperature to be derived for a fraction of cores. The protostellar and starless core mass functions (CMFs) were constructed following two different approaches, achieving a mass completeness limit of 3.7 M_⊙. Results. We retrieved 549 submillimetre cores, 316 of which are starless and mostly gravitationally bound (therefore prestellar in nature). Both the protostellar and the starless CMFs are consistent with the shape of a Salpeter initial mass function in the high-mass part of the distribution. Clustering of cores at scales of 1–6 pc is also found, hinting at fractionation of magnetised, turbulent gas.