A 2°.5 × 100° region along the celestial equator (Stripe 82) has been imaged repeatedly from 1998 to 2005 by the Sloan Digital Sky Survey (SDSS). A new catalogue of ∼4 million light-motion curves, together with over 200 derived statistical quantities, for objects in Stripe 82 brighter than r ∼21.5 has been constructed by combining these data by Bramich et al. This catalogue is at present the deepest catalogue of its kind. Extracting ∼130 000 objects with highest signal-to-noise ratio proper motions, we build a reduced proper motion diagram to illustrate the scientific promise of the catalogue. In this diagram, disc and halo subdwarfs are well-separated from the cool white dwarf sequence. Our sample of 1049 cool white dwarf candidates includes at least eight and possibly 21 new ultracool H-rich white dwarfs (Teff < 4000 K) and one new ultracool He-rich white dwarf candidate identified from their SDSS optical and UKIDSS infrared photometry. At least 10 new halo white dwarfs are also identified from their kinematics.