We present high-quality, medium-resolution X-shooter/VLT spectra in the range 300-2500nm for a sample of 12 very low mass stars in the {sigma} Orionis cluster. The sample includes eight stars with evidence of disks from Spitzer and four without disks, with masses ranging from 0.08 to 0.3M_{sun}_. 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 and the accuracy of the correlations between these secondary tracers (mainly accretion line luminosities) found in the literature. 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_{sun}_/yr down to 5x10^-11^M_{sun}_/yr, 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, which are all obtained simultaneously. In general, most of the secondary tracers correlate well with the accretion luminosity derived from the continuum excess emission. We recompute the relationships between the accretion luminosities and the line luminosities, and we confirm the validity of the correlations given in the literature, with the possible exception of H{alpha}. Metallic lines, such as the CaII IR triplet or the NaI line at 589.3nm, show a larger dispersion. 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 L_acc_ that often better agree than the uncertainties introduced by the adopted correlations. The average L_acc_ 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 nonsimultaneous observations of lines and continuum. Three stars in our sample deviate from this behavior, and we discuss them individually.