The relevance of M dwarfs in the search for potentially habitable Earth-size planets has grown significantly in the last years. In our on-going effort of comprehensively and accurately characterising confirmed and potential planet-hosting M dwarfs, in particular for the CARMENES survey, we have carried out a comprehensive multi-band photometric analysis involving spectral energy distributions, luminosities, absolute magnitudes, colours, and spectral types, from which we have derived basic astrophysical parameters. We have carefully compiled photometry in 20 passbands from the far-ultraviolet to the mi-infrared, and combined it with the latest parallactic distances and close-multiplicity information, mostly from Gaia DR2, of a sample of 2479 K5 V to L8 stars and ultracool dwarfs, including 2210 nearby, bright, M dwarfs. For that, we have made extensive use of Virtual Observatory tools. We have homogeneously computed accurate bolometric luminosities, effective temperatures of 1843 single stars, derived their radii and masses, studied the impact of metallicity, and compared our results with the literature. The over 40 000 individually-inspected magnitudes, together with the basic data and derived parameters of the stars, one by one and averaged by spectral type, have been made public to the astronomical community. In addition, we have reported 40 new close multiple systems and candidates (rho<3.3-arcsec) and 36 overluminous stars that are assigned to young Galactic populations. In the new era of exoplanet searches around M dwarfs via transit (e.g., TESS, PLATO) and radial velocity (e.g., CARMENES, NIRPS+HARPS), this work is of fundamental importance for stellar and, thus, planetary parameter determination.