We report on new nearby L and late-M dwarfs (dphot <= 30 pc) discovered in our search for nearby ultracool dwarfs (I-J >= 3.0, later than M8.0) at low Galactic latitude (|b| < 15°) over 4800 deg2 in the Deep Near Infrared Survey of the Southern Sky (DENIS) data base. We used late-M (>= M8.0), L and T dwarfs with accurate trigonometric parallaxes to calibrate the MJ versus I-J colour-luminosity relation. The resulting photometric distances have standard errors of ~15 per cent, which we used to select candidates dphot <= 30 pc. We measured proper motions from multi-epoch images found in the public archives ALADIN, DSS, 2MASS and DENIS, with at least three distinct epochs and time baselines of 10-21 yr. We then used a maximum reduced proper motion cut-off to select 28 candidates as ultracool dwarfs (M8.0-L8.0) and to reject one as a distant red star. No T dwarf candidates were found in this search, which required an object to be detected in all three DENIS bands. Our low-resolution optical spectra confirmed that 26 were indeed ultracool dwarfs, with spectral types from M8.0 to L5.5. Two contaminants and one rejected by the maximum reduced proper motion cut-off were all reddened F-K main sequence stars. 20 of these 26 ultracool dwarfs are new nearby ultracool dwarf members, three L dwarfs within 15 pc with one L3.5 at only ~10 pc. We determine a stellar density of dwarfs pc-3 mag-1 over 11.1 <= MJ <= 13.1 based on this sample of M8-L3.5 ultracool dwarfs. Our ultracool dwarf density value is in good agreement with the measurement by Cruz et al. of the ultracool dwarf density at high Galactic latitude.