We use the fundamental parameters delivered by the GES consortium in the first internal data release to select the members of γ Vel and Cha I among the UVES and GIRAFFE spectroscopic observations. A total of 140 γ Vel members and 74 Cha I members were studied. We calculated stellar luminosities through spectral energy distributions, while stellar masses were derived by comparison with evolutionary tracks. The spectral subtraction of low-activity and slowly rotating templates, which are rotationally broadened to match the vsini of the targets, enabled us to measure the equivalent widths (EWs) and the fluxes in the Hα and Hβ lines. The Hα line was also used for identifying accreting objects and for evaluating the mass accretion rate (M˙acc). The distribution of vsini for the members of γ Vel displays a peak at about 10 km s−1 with a tail toward faster rotators. There is also some indication of a different vsini distribution for the members of its two kinematical populations. Only a handful of stars in γ Vel display signatures of accretion, while many more accretors were detected in the younger Cha~I. Accreting and active stars occupy two different regions in a Teff-flux diagram and we propose a criterion for distinguishing them. We derive M˙acc in the ranges 10−11-10−9M⊙yr−1 and 10−10-10−7M⊙yr−1 for γ Vel and Cha I accretors, respectively. We find less scatter in the M˙acc−M⋆ relation derived through the Hα EWs, when compared to the Hα10%W diagnostics, in agreement with other authors