We present high-quality, medium resolution X-shooter/VLT spectra in the range 300-2500 nm for a sample of 12 very low-mass stars in the sigma Orionis cluster. The sample includes stars with masses ranging from 0.08 to 0.3 M$_odot$. The aim of this first paper is to investigate the reliability of the many accretion tracers currently used to measure the mass accretion rate in low-mass, young stars. We use our spectra to measure the accretion luminosity from the continuum excess emission in the UV and visual; the derived mass accretion rates range from 10$^{-9}$ M$_{odot}$ yr$^{-1}$ down to 5$times10^{-11}$ M$_{odot}$ yr$^{-1}$, allowing us to investigate the behavior of the accretion-driven emission lines in very-low mass accretion rate regimes. We compute the luminosity of ten accretion-driven emission lines, from the UV to the near-IR, obtained simultaneously. Most of the secondary tracers correlate well with the accretion luminosity derived from the continuum excess emission. We confirm the validity of the correlations between accretion luminosities and line luminosities given in the literature, with the possible exception of Halpha. When looking at individual objects, we find that the Hydrogen recombination lines, from the UV to the near-IR, give good and consistent measurements of accretion luminosities, often in better agreement than the uncertainties introduced by the adopted correlations. The average accretion luminosity derived from several Hydrogen lines, measured simultaneously, have a much reduced error. This suggests that some of the spread in the literature correlations may be due to the use of non-simultaneous observations of lines and continuum. Three stars in our sample deviate from this behavior, and we discuss them individually.
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