  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 H\alpha. 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.
