We present wide-field observations of the NGC 2264 molecular cloud in the dust continuum at 850 and 450{mu}m using SCUBA-2 on the James Clerk Maxwell Telescope. Using ^12^CO 3->2 molecular line data, we determine that emission from CO contaminates the 850{mu}m emission at levels ~30 per cent in localized regions associated with high-velocity molecular outflows. Much higher contamination levels of 60 per cent are seen in shocked regions near the massive star S Mon. If not removed, the levels of CO contamination would contribute an extra 13 per cent to the dust mass in NGC 2264. We use the fellwalker routine to decompose the dust into clumpy structures, and a Hessian-based routine to decompose the dust into filamentary structures. The filaments can be described as a hub-filament structure, with lower column density filaments radiating from the NGC 2264 C protocluster hub. Above mean filament column densities of 2.4x10^22^cm^-2^, star formation proceeds with the formation of two or more protostars. Below these column densities, filaments are starless, or contain only a single protostar.