The brown dwarf population in the canonical star-forming region NGC 2264 is so far poorly explored. We present a deep, multiwavelength, multiepoch survey of the star-forming cluster NGC 2264, aimed to identify young brown dwarf candidates in this region. Using criteria including optical/near-infrared (IR) colours, variability, Spitzer mid-IR colour excess, extinction, and Gaia parallax and proper motion (in order of relevance), we select 902 faint red sources with indicators of youth. Within this sample, we identify 429 brown dwarf candidates based on their IR colours. The brown dwarf candidates are estimated to span a mass range from 0.01 to 0.08 M⊙. We find rotation periods for 44 sources, 15 of which are brown dwarf candidates, ranging from 3.6 h to 6.5 d. A subset of 38 brown dwarf candidates show high-level irregular variability indicative of ongoing disc accretion, similar to the behaviour of young stars.