We present the results of a deep wide-field near-infrared survey of 12 deg2 of the Pleiades conducted as part of the United Kingdom Infrared Telescope (UKIRT) Infrared Deep Sky Survey (UKIDSS) Galactic Cluster Survey (GCS). We have extracted over 340 high-probability proper motion (PM) members down to 0.03 Msolar using a combination of UKIDSS photometry and PM measurements obtained by cross-correlating the GCS with data from the Two Micron All Sky Survey, the Isaac Newton Telescope and the Canada-France-Hawaii Telescope. Additionally, we have unearthed 73 new candidate brown dwarf (BD) members on the basis of five-band UKIDSS photometry alone. We have identified 23 substellar multiple system candidates out of 63 candidate BDs from the (Y - K, Y) and (J - K, J) colour-magnitude diagrams, yielding a binary frequency of 28-44 per cent in the 0.075-0.030 Msolar mass range. Our estimate is three times larger than the binary fractions reported from high-resolution imaging surveys of field ultracool dwarfs and Pleiades BDs. However, it is marginally consistent with our earlier `peculiar' photometric binary fraction of 50 +/- 10 per cent presented by Pinfield et al., in good agreement with the 32-45 per cent binary fraction derived from the recent Monte Carlo simulations of Maxted & Jeffries and compatible with the 26 +/- 10 per cent frequency recently estimated by Basri & Reiners. A tentative estimate of the mass ratios from photometry alone seems to support the hypothesis that binary BDs tend to reside in near equal-mass ratio systems. In addition, the recovery of four Pleiades members targeted by high-resolution imaging surveys for multiplicity studies suggests that half of the binary candidates may have separations below the resolution limit of the Hubble Space Telescope or current adaptive optics facilities at the distance of the Pleiades (a ~7 au). Finally, we have derived luminosity and mass functions from the sample of photometric candidates with membership probabilities. The mass function is well modelled by a lognormal peaking at 0.24Msolar and is in agreement with previous studies in the Pleiades. Based on observations made with the United Kingdom Infrared Telescope, operated by the Joint Astronomy Centre on behalf of the UK Particle Physics and Astronomy Research Council. E-mail: nlodieu [at] iac.es (nlodieu[at]iac[dot]es)