We present a near-infrared photometric search for unresolved substellar companions and debris discs around white dwarfs in the UKIRT Infrared Deep Sky Survey (UKIDSS) Large Area Survey. We cross-correlate the Sloan Digital Sky Survey (SDSS) DR4 and McCook & Sion catalogues of white dwarfs with the UKIDSS DR8 producing 3109 and 163 unique matches, respectively. Cooling models are fitted to the optical photometry of a subsample of DA white dwarfs and extended to the near-infrared. A comparison is then made with the observed photometry to identify those stars with a near-infrared excess consistent with the presence of a cool companion or debris disc. Where present, we have estimated the approximate spectral type of any putative companion, or an upper limit on the temperature of a debris disc. In total we identify 14-16 new candidate white dwarf + very low mass stellar systems, 9-11 candidate white dwarf + brown dwarf systems, and three candidate white dwarf + debris discs. We place lower limits on the unresolved (<2 arcsec) companions to all DA white dwarfs and thus assess the sensitivity of UKIDSS to such objects. We use this result to estimate unresolved binary fractions of f WD + dL≥ 0.4 ± 0.3 per cent, f WD + dT≥ 0.2 per cent and f WD + BD≥ 0.5 ± 0.3 per cent.