As part of a new southern sky survey for faint high proper motion stars based on Automatic Plate Measuring (APM) measurements of UK Schmidt Telescope plates, we have found a large number of previously unknown brighter objects. Spectroscopic follow-up observations with the European Southern Observatory New Technology Telescope of 15 of these new, relatively bright (12<R<15) high proper motion stars (μ>0.45arcsecyr-1) show one-third of them to be nearby (d<25pc). Among the nearby stars is an M6 dwarf with strong emission lines at a spectroscopic distance of about 11pc and an M4 dwarf at about 13pc. Coupled with earlier South African Astronomical Observatory spectroscopic observations of three similar bright high proper motion stars, the success rate of finding nearby stars (d<25pc) is about 45 per cent. All newly discovered nearby stars have disc kinematics confirmed by radial velocity measurements from our spectra. In addition there are several high-velocity stars with halo kinematics in the sample, mainly subdwarfs, at about 60 to 110pc distance. These high-velocity stars are interesting targets for further study of the Galactic escape velocity. One of the detected nearby high proper motion stars was formerly thought to be an M giant in the Small Magellanic Cloud. The spectrum of one M3 star shows a strong blue continuum, which is likely to signify the presence of a hot companion. Spectroscopic follow-up observations of high proper motion stars are shown to be an effective tool in the search for the missing stars in the Solar neighbourhood. Candidates for more extensive trigonometric parallax determination can be selected on the basis of the spectroscopic distance estimates.