We present the results of spectroscopic follow-up observations for a sample of 71 red objects with high proper motions in the range 0.08-1.14 arcsec/yr as detected using APM and SuperCOSMOS Sky Surveys (SSS) measurements of multi-epoch photographic Schmidt plates. Red objects were selected by combining the photographic BjRI magnitudes with 2MASS near-infrared JHKs magnitudes. Some 50 of the 71 spectroscopically classified objects turn out to be late-type (>M6) dwarfs and in more detail, the sample includes 35 ultracool dwarfs with spectral types between M8 and L2, some previously reported, as well as five M-type subdwarfs, including a cool esdM6 object, SSSPM J0500-5406. Distance estimates based on the spectral types and 2MASS J magnitudes place almost all of the late-type (>M6) dwarfs within 50pc, with 25 objects located inside the 25pc limit of the catalogue of nearby stars. Most of the early-type M dwarfs are located at larger distances of 100-200pc, suggesting halo kinematics for some of them. All objects with Halpha equivalent widths larger than 10 Angstroms have relatively small tangential velocities (<50km/s). Finally, some late-type but blue objects are candidate binaries.