We present the results of a deep (J = 19. 1 mag) infrared (ZYJHK) survey of three open clusters surveyed by the UKIRT Infrared Deep Sky Survey (UKIDSS) Galactic Clusters Survey (GCS) Data Release 9: the Pleiades, α Per, and Praesepe. We have selected cluster member candidates combining photometry in five near-infrared filters and proper motions derived from the multiple epochs provided by the UKIDSS GCS DR9. We provide revised membership for all previously published low-mass stars and brown dwarfs recovered by the GCS and complete the full census with new cluster member candidates. We find no evidence of K-band variability in all three clusters with mean dispersions of 0.06-0.09 mag, except for a few sources. We derive the cluster mass functions and find that their shapes are very similar and in agreement with the log-normal representation of the (system) field mass function although with some variations in the characteristic mass and dispersion values. Finally, we estimate the binary fraction of low-mass stars and brown dwarfs in Praesepe and the Pleiades, respectively, and compare them with the latest hydrodynamical simulations.