We present the results of a proper motion wide-field near-infrared survey of the entire Upper Sco (USco) association (˜160 square degrees) released as part of the United Kingdom Infrared Telescope Infrared Deep Sky (UKIDSS) Galactic Clusters Survey (GCS) Data Release 10 (DR10). We have identified a sample of ˜400 astrometric and photometric member candidates combining proper motions and photometry in five near-infrared passbands and another 286 with HK photometry and 2MASS/GCS proper motions. We also provide revised membership for all previously published USco low-mass stars and substellar members based on our selection and identify new candidates, including in regions affected by extinction. We find negligible variability between the two K-band epochs, below the 0.06 mag rms level. We estimate an upper limit of 2.2 per cent for wide common proper motions with projected physical separations less than ˜15 000 au. We derive a disc frequency for USco low-mass stars and brown dwarfs between 26 and 37 per cent, in agreement with estimates in IC 348 and σ Ori. We derive the mass function of the association and find it consistent with the (system) mass function of the solar neighbourhood and other clusters surveyed by the GCS in the 0.2-0.03 M⊙ mass range. We confirm the possible excess of brown dwarfs in USco.