Reprocessing of the primary X-ray continuum in the accretion disc is expected to cause reverberation lags which are powerful diagnostics of the geometry of the inner flow. X-ray reverberation lags are now commonly observed in supermassive accreting black hole systems (active galactic nuclei, AGN). These lags are also expected in smaller objects, where the accretor is a stellar mass black hole in a binary system (BHXRBs). However only one detection has been reported so far. I will present results obtained from a systematic analysis of X-ray lags in a sample of BHXRBs observed by XMM-Newton, with the main aim of assessing the presence of reverberation lags and study their evolution during the outburst. This study confirms the mass-scaling of the lag amplitude from supermassive down to stellar-mass black holes, supporting the hypothesis that reverberation lags are a characteristic feature of any accreting system. We find that the amplitude of the reverberation lag detected in BHXRBs scales also with the X-ray luminosity along the canonical hard state: shorter lags are observed during higher luminosity observations. This result implies that, while the source rises the hard state, reprocessing from disc radii progressively closer to the BH is observed.