  AIMS: We contribute to improving the census of cool brown dwarfs (late-T and
Y dwarfs) in the immediate solar neighbourhood. METHODS: By combining
near-infrared (NIR) data of UKIDSS with mid-infrared WISE and other available
NIR (2MASS) and red optical (SDSS $z$-band) multi-epoch data we detect high
proper motion (HPM) objects with colours typical of late spectral types
($>$T5). We use NIR low-resolution spectroscopy for the classification of new
candidates. RESULTS: We determined new proper motions for 14 known T5.5-Y0
dwarfs, many of them being significantly ($>$2-10 times) more accurate than
previous ones. We detected three new candidates, ULAS J0954+0623, ULAS
J1152+0359, and ULAS J1204-0150, by their HPMs and colours. Using previously
published and new UKIDSS positions of the known nearby T8 dwarf WISE J0254+0223
we improved its trigonometric parallax to 165$\pm$20 mas. For the three new
objects we obtained NIR spectroscopic follow-up with LBT/LUCIFER classifying
them as T5.5 and T6 dwarfs. With their estimated spectroscopic distances of
about 25-30 pc, their proper motions of about 430-650 mas/yr lead to tangential
velocities of about 50-80 km/s typical of the Galactic thin disk population.
