The discovery of \varepsilon Indi Ba , Bb , a binary brown dwarf system very close to the Sun , makes possible a concerted campaign to characterise the physical parameters of two T dwarfs . Recent observations suggest substellar atmospheric and evolutionary models may be inconsistent with observations , but there have been few conclusive tests to date . We therefore aim to characterise these benchmark brown dwarfs to place constraints on such models . We have obtained high angular resolution optical , near-infrared , and thermal-infrared imaging and medium-resolution ( up to R \sim 5 000 ) spectroscopy of \varepsilon Indi Ba , Bb with the ESO VLT and present VRIzJHKL ^ { \prime } M ^ { \prime } broad-band photometry and 0.63–5.1 \mu m spectroscopy of the individual components . The photometry and spectroscopy of the two partially blended sources were extracted with a custom algorithm . Furthermore , we use deep AO-imaging to place upper limits on the ( model-dependent ) mass of any further system members . We derive luminosities of log L/L _ { \sun } = -4.699 \pm 0.017 and -5.232 \pm 0.020 for \varepsilon Indi Ba , Bb , respectively , and using the dynamical system mass and COND03 evolutionary models predict a system age of 3.7–4.3 Gyr , in excess of previous estimates and recent predictions from observations of these brown dwarfs . Moreover , the effective temperatures of 1352–1385 K and 976–1011 K predicted from the COND03 evolutionary models , for \varepsilon Indi Ba and Bb respectively , are in disagreement with those derived from the comparison of our data with the BT-Settl atmospheric models where we find effective temperatures of 1300–1340 K and 880–940 K , for \varepsilon Indi Ba and Bb respectively , with surface gravities of log g=5.25 and 5.50 . Finally , we show that spectroscopically determined effective temperatures and surface gravities for ultra-cool dwarfs can lead to underestimated masses even where precise luminosity constraints are available . The full resolution spectra of both brown dwarfs are available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr