Context. Blue compact galaxies (BCG) are gas-rich, low-luminosity, low-metallicity systems that undergo a violent burst of star formation. These galaxies offer us a unique opportunity to investigate collective star formation and its effects on galaxy evolution in a relatively simple environment. Spatially resolved spectrophotometric studies of BCGs are essential for a better understanding of the role of starburst-driven feedback processes on the kinematical and chemical evolution of low-mass galaxies near and far. Aims: We carry out an integral field spectroscopic study of a sample of BCGs, with the aim of probing the morphology, kinematics, dust extinction, and excitation mechanisms of their warm interstellar medium. Methods: Eight BCGs were observed with the VIMOS integral field unit at the Very Large Telescope using blue and orange grisms in high-resolution mode. At a spatial sampling of 0''&dotbelow;67 per spaxel, we covered about 30″ × 30″ on the sky, with a wavelength range of 4150...7400 Å. Emission lines were fitted with a single Gaussian profile to measure their wavelength, flux, and width. From these data we built two-dimensional maps of the continuum and the most prominent emission-lines, as well as diagnostic line ratios, extinction, and kinematic maps. Results: An atlas has been produced with the following: emission-line fluxes and continuum emission; ionization, interstellar extinction, and electron density maps from line ratios; velocity and velocity dispersion fields. From integrated spectroscopy, it includes tables of the extinction corrected line fluxes and equivalent widths, diagnostic-line ratios, physical parameters, and the abundances for the brightest star-forming knots and for the whole galaxy. Based on observations made with ESO Telescopes at the Paranal Observatory under program ID 079.B-0445.The reduced datacubes and their error maps (FITS files) are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/577/A21