We present parallax observations and a detailed model atmosphere analysis of 54 cool and ultracool (Teff<4000K) white dwarfs (WDs) in the solar neighbourhood. For the first time, a large number of cool and ultracool WDs have distance and tangential velocities measurements available. Our targets have distances ranging from 21pc to >100pc, and include five stars within 30pc. Contrary to expectations, all but two of them have tangential velocities smaller than 150km/s thus suggesting Galactic disc membership. The oldest WDs in this sample have WD cooling ages of 10Gyr, providing a firm lower limit to the age of the thick disc population. Many of our targets have uncharacteristically large radii, indicating that they are low-mass WDs. It appears that we have detected the brighter population of cool and ultracool WDs near the Sun. The fainter population of ultracool CO-core WDs remain to be discovered in large numbers. The Large Synoptic Survey Telescope should find these elusive, more massive ultracool WDs in the solar neighbourhood.