We report the discovery of twenty-one hitherto unknown bright southern ultracool dwarfs with spectral types in the range M7 to L5.5, together with new observations of a further three late M dwarfs previously confirmed. Three more objects are already identified in the literature as high proper motion stars;we derive their spectral types for the first time. All objects were selected from the 2MASS All Sky and SuperCOSMOS point source databases on the basis of their optical/near-infrared colours, $J$-band magnitudes and proper motions. Low resolution (R $sim$ 1000) $JH$ spectroscopy with the ESO/NTT SOFI spectrograph has confirmed the ultracool nature of 24 targets, out of a total of 25 candidates observed. Spectral types are derived by direct comparison with template objects and compared to results from H$_2$O and FeH indices. We also report the discovery of one binary, as revealed by SOFI acquisition imaging; spectra were taken for both components. The spectral types of the two components are L2 and L4 and the distance $sim$ 19 pc. Spectroscopic distances and transverse velocities are derived for the sample. Two $sim$ L5 objects lie only $sim$ 10 pc distant. Such nearby objects are excellent targets for further study to derive their parallaxes and to search for fainter, later companions with AO and/or methane imaging.