We present VLT/X-shooter observations of a sample of 36 accreting low-mass stellar and substellar objects (YSOs) in the Lupus star-forming region, spanning a range in mass from similar0.03 to similar1.2 M, but mostly with 0.1 M<Msub *< 0.5 M. Our aim is twofold: firstly, to analyse the relationship between excess-continuum and line emission accretion diagnostics, and, secondly, to investigate the accretion properties in terms of the physical properties of the central object. The accretion luminosity (Lsubacc), and in turn the accretion rate (Msubacc ), was derived by modelling the excess emission from the UV to the near-infrared as the continuum emission of a slab of hydrogen. A number of properties indicate that the physical conditions of the accreting gas are similar over more than 5 orders of magnitude in Msubacc, confirming previous suggestions that the geometry of the accretion flow controls the rate at which the disc material accretes onto the central star.