We investigate whether there is any correlation between the X-ray afterglow luminosity and the prompt emission properties of a carefully selected sub-sample of bright Swift long Gamma-ray bursts (GRBs) nearly complete in redshift (∼90 per cent). Being free of selection effects (except flux limit), this sample provides the possibility to compare the rest frame physical properties of GRB prompt and afterglow emission in an unbiased way. The afterglow X-ray luminosities are computed at four different rest frame times (5 min, 1 h, 11 h and 24 h after trigger) and compared with the prompt emission isotropic energy Eiso, the isotropic peak luminosity Liso and the rest frame peak energy Epeak. We find that the rest frame afterglow X-ray luminosity do correlate with these prompt emission quantities, but the significance of each correlation decreases over time. This result is in agreement with the idea that the GRB X-ray light curve can be described as the result of a combination of different components whose relative contribution and weight change with time, with the prompt and afterglow emission dominating at early and late time, respectively. In particular, we found evidence that the plateau and the shallow decay phase often observed in GRB X-ray light curves are powered by activity from the central engine. The existence of the LX - Eiso correlation at late times () suggests a similar radiative efficiency among different bursts with on average about 6 per cent of the total kinetic energy powering the prompt emission.